Oviedo, formerly known as Leo Nunez, had Tommy John surgery in September and is unlikely to pitch in the Majors this season. The Rays will likely place him on the 60-day disabled list.
"[Gomes] nailed Spring Training. He might have had the best Spring Training of any pitcher in camp," Rays manager Joe Maddon said. "But looking at the macro situation, you have to look at the whole thing. We decided this is the best way to go right now."
Gomes felt like he did all he could to make the team.
"I threw the ball well," Gomes said. "I felt great all spring. It's a good sign going into the rest of the year. That's something I feel I can sustain. So keep going, keep doing what I've been doing and stay ready."
Tampa Bay's bullpen to begin the season will be as follows: Fernando Rodney, Joel Peralta, Jake McGee, Cesar Ramos, Kyle Farnsworth, Jamey Wright and the loser of the Roberto Hernandez/Jeff Niemann competition for the No. 5 spot.
Gomes basically lost out to veteran right-hander Wright, who signed a Minor League contract on Jan. 22.
"Honestly, the deal there is just trying to deal with the people that are available to you the best you possibly can at the moment," Maddon said. "I'm talking about depth. Brandon Gomes is good enough -- better than good enough -- to be a Major League pitcher today. He deserves to be a Major League pitcher today. And he could be a very productive Major League pitcher today. But right now we don't have that particular job for him at this moment.
"The flip side, again, I think Jamey Wright is going to pitch a lot better than what you saw in this Spring Training. It's a situation for us where this is kind of how we looked at it in the offseason working out."
Gomes said he understood the situation.
"It's just how it goes sometimes. It's how the game works," Gomes said. "Just go down there and stay ready for whenever the opportunity comes for me to come back up here."
The rest of the Opening Day roster will be as follows:
Outfielders: Sam Fuld, Desmond Jennings, Ben Zobrist, and Matt Joyce
Infielders: Evan Longoria, Yunel Escobar, Ryan Roberts, Kelly Johnson, Sean Rodriguez, James Loney
DH: Luke Scott
Catchers: Jose Molina and Jose Lobaton
Starting rotation: David Price, Jeremy Hellickson, Matt Moore, Alex Cobb, and Hernandez/Niemann.