Lenders extended $2.4 trillion in home loans last year, the most since 2006, according to industry research group Inside Mortgage Finance. That was also a 46% increase from 2018.

Robust mortgage lending is generally a good sign for housing, which has seen a rebound in price growth and home sales after a period of declining gains. A refinancing frenzy, induced by last year’s trio of interest-rate cuts, fueled the mortgage making and helped steady the industry. The refinancing boom also bodes well for the broader economy, since homeowners saving on their monthly mortgage payments are likely to spend more on goods and services.

“When a large and cyclical part of the economy—housing—is starting to improve, it’s a good sign for the economy at large,” said Sam Khater, chief economist of mortgage-finance giant Freddie Mac.

The Mortgage Bankers Association estimates that refinancings made up 38% of mortgage originations last year.

Kristen Devlin and her husband decided to refinance their south-central Pennsylvania home last fall while trying to pay down a pile of medical bills.

Their rate dropped from 6.25% to 4.99%, cutting their monthly payment. The couple managed to pay down their medical bills and chose to keep paying their prerefinancing payment of $1,250 for their three-bedroom, three-bathroom house. The move will shave six years off their mortgage term.

“I was very pleased to save money and proud of successfully adulting,” Mrs. Devlin said.

In Philadelphia, Annie Heckenberger’s older brother told her it would be smart to refinance the house she bought about a year earlier. His advice helped her lock in a new rate of 3.88%, more than a percentage point lower than her original one.

“It was more paperwork than I anticipated but worth it in savings,” Ms. Heckenberger said.

The average rate on the 30-year fixed-rate mortgage, the most popular home loan in the U.S., dropped to 3.74% at the end of 2019, down from 4.55% a year earlier. Freddie Mac said Thursday that the average rate is now around 3.6%, its lowest level in more than three months.

Mortgage making accelerated at the end of the year. Last year’s fourth-quarter totals were the biggest quarter since the third quarter of 2005.

December sales of existing homes jumped nearly 11% from the year before, according to the National Association of Realtors. The NAR said, though, that the year-earlier period had been a particularly weak month for sales in part because of buyers’ uncertainty around the federal government shutdown.

But the uptick in mortgage lending doesn’t mean buyers will have an easy time this spring. Major barriers including a lack of housing supply and relatively tight bank-lending standards are pushing homeownership out of reach for many Americans.

Home prices continue to rise faster than incomes, fueling concerns that affordability will remain an issue for buyers, especially those looking to buy for the first time. And the tight supply that has choked popular coastal markets has started to seep into other cities like Boise and Philadelphia that have traditionally been considered more affordable.

Low rates aren’t always entirely good for those first-time buyers. Low rates can also inflate home prices, since borrowers can afford bigger mortgages and might bid more for homes than they otherwise would.

It isn’t clear how long the mortgage boom will last. Refinancings are expected to decline through 2021, dragging down overall mortgage volume, according to estimates from the Mortgage Bankers Association.

Still, an expectation that interest rates will hold steady or even keep falling is a good sign for mortgage lending in 2020, analysts said. Some mortgage brokers said last year’s boom is extending into the new year.

“It’s very likely that the first quarter or first half of 2020 will be bigger than the first half of 2019,” said Guy Cecala, chief executive of Inside Mortgage Finance. “People are encouraged by lower rates.”

Tim Lindsey, an originating branch manager at CrossCountry Mortgage in Greenwood Village, Colo., said the number of mortgages he processed grew more than 25% last year. Mr. Lindsey said he hasn’t had a day off since New Year’s Day.

“There was an incredibly large amount of origination from previous years,” Mr. Lindsey said. “Everyone I know had their best year ever.”

Write to Orla McCaffrey at [email protected]