Gomes, 30, was hitting .211 with 11 home runs and 31 RBIs this season with Cincinnati. His best season came last year, when he drove in a career-high 86 runs for the Reds.
Gomes is looked upon as a right-handed power hitter off the bench. He will also platoon with Laynce Nix in left field. He has a career .281 batting average against left-handers.
"We have been looking for a big right-handed bat off the bench. He is probably a little bit more than that," Johnson said. "He is going to get some playing time in left field. We just need to spark the offense. Hopefully, he will give us some of that."
Gomes admitted that he was not happy about leaving the Reds.
"I gave it a great run. I'm bitter about leaving, because I really love these guys," Gomes said. "I love where this team is at. I love where they're about to go. As we see right now, it's a business. On the other token, a team reached out and wanted my services. I take that as a compliment, as well."
Nix said he is pleased to be reunited with his old teammate from Cincinnati. They played together in 2009-10.
"I was a little surprised. Jonny is a great guy. I think he will add a lot to this clubhouse, a lot of personality," Nix said. "He is a go-getter. I'm excited."
Gomes is a career .244 hitter (554-for-2,274) with 115 home runs and 352 RBIs in 738 career games spanning portions of nine big league seasons spent with the Reds (2009-11) and Rays. He has averaged more than 17 home runs per campaign since 2005, despite only receiving more than 400 at-bats once. Three times since '05, Gomes hit 20 or more home runs in a single season.
At the time of the trade, Rhinehart, 26, was batting .283 with 59 RBIs in 89 games with Double-A Harrisburg. Manno, 22, earned 12 saves in 34 appearances this year with Hagerstown of the Class A South Atlantic League.
To make room for Gomes, the Nationals will have to make a roster move, which will be announced Wednesday.