Finnegan missed more than two months due to left shoulder issues. He allowed four runs over five innings Wednesday night in a rehab start for Triple-A Louisville, and he produced a 3.00 ERA in three rehab outings.
To make room on the roster, the Reds optioned right-hander Lisalverto Bonilla to Triple-A Louisville and also transferred right-hander Bronson Arroyo (right shoulder) to the 60-day disabled list.
Finnegan suffered the first major injury of his career in his third start of the season on April 15.
The 24-year-old Finnegan traveled with the Reds to Washington for their final two games in the series against the Nationals.
"I was really excited to walk in, see all the guys and give them a hug and tell them what's up," Finnegan told reporters Sunday. "I had to go through a whole pretty much second spring training, that was the worst part about it.
"It was definitely tough. It's tough to put into words how upset and mad I was. I couldn't at least do something to help these guys out when they needed it or just try to do something for the team. But hopefully Monday will change that."
Finnegan is 1-0 with a 2.70 ERA over 10 innings in his three starts this season. He owns a 16-14 career record with a 3.76 ERA in a 61 games (38 starts) with the Kansas City Royals and Reds. He was acquired from Kansas City at the 2015 trade deadline.
Bonilla, 27, is 1-3 with a 7.59 ERA over 32 innings in eight appearances (four starts) with the Reds this season.
The 40-year-old Arroyo told reporters last week his 16-year major league career might be over as he deals with a strained right shoulder.