Parra, 30, spent his entire pro career in the Brewers organization, including five seasons in the Majors. He was thrilled to be joining a former National League Central rival.
"I was excited, especially when I heard they were interested," Parra told MLB.com. "I'm excited to have an opportunity with a team that's doing so well. I always had a ton of respect when playing against them and now I am looking forward to playing for them."
Originally a prized young starting pitcher who once threw a perfect game in Triple-A, Parra didn't develop into the ace Milwaukee hoped for. He was to be moved to the bullpen in 2011 but missed the entire season with a sprained elbow ligament and back issues.
In 2012, Parra was 2-3 with a 5.06 ERA in a career-high 62 appearances while earning $1.2 million. He was arbitration-eligible this winter and the Brewers did not tender him a contract, which made him a free agent.
"For missing all of 2011, I was happy with how I handled it," Parra said of being in the bullpen. "I'm looking to build on that."
Earlier in the winter, Reds general manager Walt Jocketty indicated he would keep an eye on the market for a left-handed reliever. With just under two weeks left until Spring Training camps open, prices are likely falling for free agents.
After they moved Aroldis Chapman to the rotation this offseason, the Reds had only Sean Marshall from the left side in their bullpen heading into 2013. If Parra is successful, he would make the Majors' best bullpen last season even stronger. Lefty hitters batted .229 against Parra last season.
Parra said he and the Reds have discussed philosophies and how he might be used but wanted to meet face-to-face with pitching coach Bryan Price. A resident of nearby Scottsdale, Ariz., Parra expected to arrive early at Reds camp in Goodyear on Monday.
"We've discussed but I'd like to hear Bryan say it," Parra said. "I can go multiple innings if needed and face guys on both sides of the plate. I've always done it. But I won't concern myself with the role. I just want to get out there pitching and see what happens."
Besides having two separate tours with the Mariners, the 34-year-old Olivo has also played for the White Sox, Padres, Marlins, Rockies and Royals. His last two seasons were spent in Seattle, where he batted .222 with 12 home runs and 29 RBIs in 87 games during 2012.
Lifetime, Olivo is a .241 hitter with a .275 on-base percentage.
Cincinnati enters camp with veteran Ryan Hanigan as the primary catcher and Devin Mesoraco backing up. The team expects to have 28 pitchers report on Feb. 12, and they will all need someone to throw to behind the plate. Olivo's addition will give the Reds six catchers in camp.