WASHINGTON—Seniors and other Americans receiving Social Security will see the largest increase to their benefits in seven years in January, a bit of relief that for the first time in years won’t be largely consumed by higher health-care costs.

The 2019 cost-of-living increase will be 2.8%, the Social Security Administration announced Thursday, which translates into an average increase in retiree benefits of about $40 a month. More than 62 million Americans receive Social Security benefits, most of them retirees.

While...