Elliot Swart spent his last day in Boston in June packing up his Jeep Wrangler for a four-day, one-way road trip to Phoenix.

Mr. Swart had been renting a one-bedroom apartment in the Prudential Center, which also was where 3Derm, the medical-software startup he co-founded, was based. When the coronavirus pandemic shut down his office, Mr. Swart, in the process of putting together a permanent remote engineering team, saw the opportunity for a major reboot.

"I always knew I loved Phoenix," said Mr. Swart, who is 29 and now the chief architect of Digital Diagnostics, which acquired 3Derm in August. "I love off-roading, I love the desert. I wanted to stop living life on hard mode, but at the same time, I still wanted a city with all the trappings of modernity."

Just before New Year’s Eve, he closed on a four-bedroom home built into a mountain cliff with views of downtown Phoenix for $932,000. The home, in a gated community near North Mountain Park, has vaulted ceilings, a master suite with a balcony and a spacious wraparound patio with a cascading waterfall.

"It’s near Sunnyslope, a neighborhood with a very good amount of socioeconomic diversity and plenty of shops and places to eat five-to-seven minutes away," Mr. Swart said. "As someone who is multiracial myself, it’s nice to be in a place where I don’t stand out like a sore thumb."

America’s fifth-most populous city, Phoenix also is one of the fastest-growing. Between 2010 and 2019, it saw the highest numeric increase in population of any city, according to the U.S. Census Bureau. Nearly 1.7 million people were living there in 2019.

Phoenix has continued to draw new residents through the pandemic, in part because of levels of job and wage growth well above the national average, according to the nonprofit Milken Institute, an economic think tank. Housing permits in the Phoenix metropolitan area—which includes Mesa and Scottsdale—were up by nearly 30% in September over the previous year.

Now, Phoenix is drawing record numbers of luxury-home buyers—even as summers there grow ever-more scorching. Temperatures hit 100 degrees and higher a record-breaking 145 days last year.

Many, like Mr. Swart, are relocating from other parts of the country where prices for comparable homes are much higher. "In Boston, you pretty much have to take a company public in order to buy a nice house and feel comfortable," he said. "I’m paying less for mortgage than I did for rent for my one-bedroom."

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Mr. Swart now has space for a home office and family heirlooms, like the desk made from a swing that once hung inside his great-grandparents’ home in India.

In 2020, 3,233 homes priced at $1 million or more were sold in the Phoenix-Mesa-Scottsdale metropolitan area, a 56% jump from 2019, according to Realtor.com. Those sales far outpaced other single-family home sales, which saw an 8% growth overall. (News Corp, owner of The Wall Street Journal, also operates Realtor.com under license from the National Association of Realtors.)

Luxury home guest casita in the southwest USA. (iStock)

Overall, prices for luxury homes—the top 5% of the market—have surged nearly 40% since 2015. And the competition for those homes is fierce.

"I’ve never seen as low active inventory as I have in the last six months," said Jay Macklin, a broker with Corcoran Platinum Living in Scottsdale, who said that more than 40% of the luxury-home buyers he is working with now are from other states, particularly California and Oregon.

"There’s a lot of escalation—bidding over asking price, waiving inspections, waiving appraisals," he added. "Those are not great ideas, but people are willing to do a lot right now to find a house."

Mr. Macklin also is going the extra mile: He has created a dozen customized video cards that he has begun sending out to owners of desirable properties that aren’t on the market, with a personalized appeal to consider selling. "We’re putting it in a FedEx package with a letter from a buyer—‘I’m looking in your neighborhood, your home matches exactly what I’m looking for’—and an offer," he said. "We’re trying to think out of the box."

Jared Peterson, regional vice president of Bay Equity Home Loans in Grand Junction, Colo., closed on a $1.9 million home in the Phoenix suburb of Cave Creek in late March after a fierce bidding war. Mr. Peterson, 48 years old and a single parent, bought the four-bedroom house as a winter getaway after initially considering vacation homes in Fort Myers, Fla.

Phoenix, just an hour’s flight from his home in Grand Junction, won him over with its dry, sunny climate and cosmopolitan vibe. Plus, his girlfriend lives there.

"I’m a foodie. There are great places to eat. And retail is still amazing there," he said. "Phoenix has the draw of all that…but it doesn’t have the big-city feel."

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The listing for the 4,121-square-foot home, which has a great room with retractable doors that open onto shaded patios and a large saltwater pool, went active on the last night of a weeklong house-hunting trip that Mr. Peterson took with his two teenage children. Although the Petersons had been planning to spend their last day by the pool, they hustled over.

"We went out there Sunday morning knowing [the seller] already had two offers, one all cash," Mr. Peterson said. "I was trying to keep my budget under $1.5 million…but things were going up in price even in the eight days we were there. It did turn into a bit of a bidding war, but we had it by Sunday night."

Phoenix’s popularity as a vacation destination has fueled the market for investment properties. "There are a lot of investors buying luxury homes to list on Airbnb, " said Sacha Blanchet, a real-estate sales associate with Coldwell Banker Realty in Phoenix. There are few restrictions on short-term rentals, although owners of vacation properties must register with the city.

Chris Jones, a real-estate agent with the Brokery in Phoenix, and his partner bought a 5,000-square-foot house near Phoenix Mountains Preserve for $1.675 million in July 2019, with the plan of relocating there from San Francisco, where they own an apartment.

Luxury home backyard pool area in the evening. (iStock)

Mr. Jones, 27, spent the following 18 months remodeling the home, which has four bedrooms, a large chef’s kitchen, a heated pool and a putting green, at a cost of about $300,000. Now, instead of living there, he is renting the house out for $1,300 a night on Airbnb and crashing in his parents’ Phoenix guesthouse.

"We would love to be here full time, but the rental market is too good—it’s absolute insanity," said Mr. Jones, who is splitting his time between Phoenix and San Francisco. "A lot of people are coming for extended-stay vacations. There have been less [Covid-related] restrictions and there’s good weather, you can eat outside and go hiking."

Phoenix’s business climate was the prime draw for Daxs Stadjuhar, 47, a managing partner in a financial-services firm.

He moved with his wife, Kerry Stadjuhar, and their four children from Sacramento, Calif., to a $1.35 million home in North Scottsdale in March 2020.

Mr. Stadjuhar’s firm, based in northern California, was seeking to expand to other regions of the country. Ms. Stadjuhar, 46, home-schooled the children even before the pandemic, which gave the family greater flexibility to relocate.

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"Phoenix was a great hub to do business," said Mr. Stadjuhar, adding that his parents also live there.

The Stadjuhars’ five-bedroom home, which has nearly 4,300 square feet of living space, a pool and an in-ground trampoline, has been a haven throughout the pandemic.

The great room has been converted into a classroom for the kids. Mr. Stadjuhar’s office is at the opposite end of the house, "as far away as possible," he said.

The children also spend part of each day doing classwork outside on the shaded patio, where the Stadjuhars have set up a Ping-Pong table and a large magnetic chessboard. Owls and Harris’s Hawks pay visits to their backyard, and javelinas occasionally wander by. Ms. Stadjuhar said the children have become interested in learning about animals since the move.

"It does get very hot, but we are doing more things outdoors here than we did in California," she said. "We get out walking more, and my daughter and two younger sons and I have started horseback riding."

The Stadjuhars’ home is within a half-hour’s drive of Phoenix Sky Harbor Airport. Mr. Stadjuhar had planned to spend much of the past year traveling to recruit new clients, but it hasn’t worked out that way. "Half the conversations I had, when people found out I live in Scottsdale, [were], ‘Hey, I’ll visit you,’" he said.

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