Yahoo! Sports reports that Richards will receive a two-year contract that includes $15 million guaranteed.
Richards, 30, is likely to spend the entire 2019 season recovering from Tommy John surgery, the latest setback in a career littered with them for the right-hander.
He made 16 starts to begin 2018 -- posting a 3.66 ERA, a 1.28 WHIP and a 2.56 strikeout-to-walk ratio -- but damaged his ulnar collateral ligament for a second time in July.
"A lot of guys come back from this surgery and they have long careers," Richards said in July. "Hopefully, this adds a few years on the end of my career. I'll be back. Everything will be fine. I'll get through this."
The Angels had high hopes for Richards when they drafted him with the 42nd overall pick out of Oklahoma in 2009. He finally cashed in on those expectations in 2014, using a lively, high-90s fastball and a devastating slider to post a 2.53 ERA with 164 strikeouts in his first 167 innings.
But Richards tore his left patellar tendon while covering first base at Fenway Park on Aug. 20, prematurely ending an upstart season. He stayed healthy in 2015 -- going 15-12 with a 3.65 ERA in 32 starts -- but compiled only 138⅔ innings in the three seasons that followed.
Early in the 2016 season, Richards was diagnosed with a torn ligament in his pitching elbow and spent the rest of the year rehabbing through stem-cell therapy. He also missed five months in 2017 because of a nerve irritation in his right biceps.
ESPN's Alden Gonzalez contributed to this report.