From Europe to Asia and North America, people have been moving across borders in record numbers, lured by tight labor markets and looser post-Covid travel rules. Many are landing in cities where housing is in short supply.

That is helping push up rents and keep home prices from falling as much as expected despite sharp increases in borrowing costs, especially in Europe, Canada and Australia.

In Canada, which absorbed a record 437,000 migrants last year, property prices started rising again in February after 10 straight monthly declines. In the U.K., annual inflation in rents in May hit its highest level since records began in 2016, and has accelerated for 20 of the past 21 months.

In the U.S., rent growth is slowing, but home prices have started rising again after falling over the past year. The median U.S. existing-home sales price bottomed at $361,200 in January and has risen each month since, according to National Association of Realtors data, though they are still down year-over-year.

Rent and housing costs continue to be a driver of inflation in the U.S., accounting for 70% of the 0.2% increase in consumer prices during June.

Many factors, including underinvestment in supply of new houses, and a reluctance by some owners to sell, are helping keep housing costs elevated in the U.S. Still, some economists say the arrival of so many legal and illegal immigrants is also part of the equation. The U.S. population grew by 1.26 million people last year, the fastest rate since 2019, with almost all of the increase—one million—coming from immigrants.

A recent Goldman Sachs report pointed to immigration as a key reason why house prices in major economies have shown signs of leveling out at higher prices than expected following declines sparked by interest-rate hikes.

“A post-pandemic recovery in immigration appears to be boosting population growth, thereby lifting housing demand and limiting house price downside,” economists Joseph Briggs and Giovanni Pierdomenico wrote. Prices have rallied the most in Australia and Canada, where immigration and population growth have rebounded most strongly, they wrote.

For property owners and landlords, support from immigration is good news, limiting downsides from slowing economic growth. A sharp decline in housing costs—which is still possible if interest rates keep climbing—would be destabilizing to the world economy.

But for many people, the persistence of high housing costs is fueling frustration, especially when so many other expenses are rising.

Scott and Dianne Wilson have watched rents accelerate through 2023 as they finalize a move with their two young sons from the U.K. to Brisbane, Australia, where Ms. Wilson has secured work as a child-care educator. They hope to move in August and are looking at paying $2,000 a month for a family home that their relocation agent tells them would have cost about $1,400 last year.

“The majority of the stuff that’s been coming through has been really, really dated. I can only describe them as 1970s style,” Mr. Wilson said, citing kitchens with avocado-green countertops. The couple are scouring online crime statistics to identify more affordable, yet still livable, neighborhoods.

Since housing costs—especially rents—make up an important part of central banks’ inflation gauges, their stickiness is adding ballast to arguments to raise interest rates further.

Central banks in Australia and Canada have surprised investors with interest-rate increases recently.

Around five million more people moved to affluent countries last year than left them, the Journal recently reported, up 80% from pre-pandemic levels. Germany, Canada, Japan and other countries are rewriting immigration rules to bring in more people to fill skills shortages.

Economists estimate that around 85% of migrants become tenants after arriving in a country, meaning the pressure they exert on housing costs is strongest in the rental market, though some also ultimately purchase homes.

In Australia, whose borders were largely closed during the pandemic, around 400,000 more people arrived during the 12 months through June than left, according to official forecasts—nearly double the pre-pandemic average. Officials expect another 315,000 immigrants in the 12 months through June 2024, in a country of roughly 26 million people.

The influx prompted Philip Lowe, Australia’s central bank governor, in May to sound the alarm on inflation as migrants search for somewhere to live.

Average rents across Australia’s major cities increased 11.5% over the 12 months through June and are more than 25% up on pre-pandemic levels, according to property analytics provider CoreLogic. Home prices recently began rising again on a month-over-month basis after falling 9.1% over the seven months through February.

“The population is increasing by 2% this year. Are there 2% more houses? No,” Lowe said.

Australian property agents say queues for recent viewings have often been so long that many would-be tenants walked away before even getting inside. They expect another surge in real-estate demand as overseas students arrive following the conclusion of the Northern Hemisphere’s academic year.

“I’ve really no idea where you’re going to house them,” said Diana Vescio, who works in real estate in Sydney.

Some landlords have hiked rents to recoup money lost at the height of the pandemic, said Vescio, recalling a period when some tenants defaulted, negotiated lower rents, or moved to cheaper locations. Others are trying to pay their home loans, whose costs have increased, she said.

Many economists had tipped Australian house prices to fall by 20% when the Reserve Bank of Australia began its program of aggressive rate rises in May 2022.

Instead, in Sydney, a landing point for many migrants, home values have risen by 6.7%, from recent lows, the equivalent of a $45,000 lift in the median dwelling value.

The average house price in Sydney is likely to rise 6-9% over the 12 months through June 2024, as few people put their house up for sale and the city’s population grows, according to Australian property classifieds group Domain. Across Australia, it predicts migration will drive demand for 300,000 more dwellings.

The additional strain migration places on housing supply could mean that the Reserve Bank, which has raised the country’s cash rate by 4 percentage points since May 2022 to its highest level in more than 11 years, keeps raising interest rates.

“The risk is that it could be inflationary, prompting tighter monetary settings than otherwise,” HSBC economist Paul Bloxham said.

Germany, too, is seeing rents rise against a backdrop of increased migration and slow construction. An influx of more than 1.1 million refugees from the Ukraine war helped net migration hit a record 1.5 million in 2022, while the country built fewer than 75% of the 400,000 new apartments targeted annually by the government to address shortages.

Annual rent growth in Germany accelerated in the first quarter of 2023, with quarterly growth hitting record levels in Berlin and Stuttgart, according to data from real-estate platform ImmoScout24. Punishing rent increases in the country’s seven largest metropolises were pushing many would-be renters into surrounding areas, it said.

Many economists argue the best response is more construction. In the U.K., new housing supply peaked in 2020, and has fallen short of a government target for 300,000 new homes a year ever since, partly due to pandemic disruptions.

Australia’s government in May said it would soon introduce tax breaks to boost supply of rental accommodation, while raising rental assistance payments to low-income groups.

But construction can take years, partly because of tight planning regulations.

Write to Stuart Condie at stuart.condie@wsj.com