WYOMING, Mich.—Like many adults with disabilities, Nathan Mort has often struggled to find and hold a job. A conservation group once declined his attempt to volunteer. The 37-year-old West Michigan native, who has a high-functioning form of autism, ended up living with his parents and dependent on government payments.

His fortunes turned several years ago when a local food distributor, Gordon Food Service, found itself short of entry-level workers and developed an internship program for adults with disabilities. Mr. Mort was hired from the program permanently to track warranty claims for the company’s trucks and other equipment. That allowed him to stop collecting federal disability benefits and move into his own home.

“A reason why I like my job is because it’s kind of the same thing over and over again. I really like routines. That is part of my autism,” Mr. Mort said. Making his own money, he added, “makes you feel more worth something.”

Mr. Mort is part of a wave of disabled Americans joining or returning to the U.S. labor force, breaking a long-running trend that had pushed millions to the sidelines of work. These workers have benefited from a tight economy with a very low overall unemployment rate—3.9% in December, just above lowest level since 1969—as employers in many sectors tackle a shortage of available workers by becoming more creative about whom they recruit.

The number of American workers receiving federal disability benefits dropped to 8.5 million in December from a peak of 9 million four years earlier as the share of disabled Americans in the labor force rises. The average monthly jobless rate for the disabled in 2018 was 8%, down 4.6 percentage points from 2014. Unemployment for this group is falling at a faster rate than for the broader population.