TORONTO -- The Blue Jays' struggling bullpen received some additional help on Tuesday evening when the club acquired veteran reliever Jason Grilli and cash considerations from the Braves for pitching prospect Sean Ratcliffe.

Grilli got off to a rough start this season after he returned from tearing his left Achilles tendon last July. He allowed 11 runs -- 10 earned -- in his first 12 1/3 innings but has pitched better over the last two weeks and hasn't allowed a run over his past five appearances (4 2/3 innings).

The 39-year-old has spent parts of 14 years in the big leagues, and he's a former closer for both the Braves and Pirates. He could potentially enter the mix as a setup man in Toronto as the club continues to search for answers on how to bridge the gap to closer Roberto Osuna.

"We've been looking for help from the day I got here to complement our team," Blue Jays general manager Ross Atkins said. "There is a lot that we like about Jason and how he complements this team. The first thing that comes to mind is experience.

"He has been on winning teams, in very high-leverage situations, and gets a ton of swing and miss, has gotten a lot of swing and miss in his career. Those are good attributes for someone to be in the bullpen."

The Blue Jays' bullpen entered play on Tuesday ranked third worst in the Major Leagues by allowing 41.3 percent of inherited runners to score. Toronto also ranked 10th in the American League with a 3.89 ERA, 12th with a 1.34 WHIP and the bullpen's 20 home runs allowed were tied for the fifth most in the AL.

Grilli spent most of his career throwing in the mid-90s, but according to BrooksBaseball.net, his velocity dropped this season to an average of 92 mph. He averaged 12.0 strikeouts per nine innings last year and has a rate of 12.2 in 2016. One sign of concern this season is that Grilli has also walked 6.9 batters per nine innings.

Toronto began the year with Drew Storen and Brett Cecil as its primary setup men. Cecil has been placed on the disabled list and is out until at least the middle of June, while Storen has struggled with a 6.75 ERA in 17 1/3 innings. Storen has lost most of his high-leverage opportunities, with Gavin Floyd and Jesse Chavez having assumed bigger roles with the club.

"I think so, on some levels," Atkins said when asked about whether the lack of strikeouts was something he felt needed to be addressed. "Our bullpen, there's a lot of individual pieces and there's a lot of talent in our bullpen. Swing and miss is definitely going to be valuable, but one of the things we've really been lacking is experience. That component with his ability to miss bats is attractive."

Ratcliffe is a 21-year-old from Ajax, Ontario, who spent last season with Class A Vancouver. He posted a 3.60 ERA while striking out 30 over 40 innings, all but one of his 22 appearances coming out of the bullpen.

Toronto did not release the amount of cash that would be exchanging hands as part of the deal, but reportedly Atlanta will remain on the hook for all but the league minimum. Atkins conceded the financial element was a big selling point of the deal.

"We need to stay flexible and we need to make sure that we can continue to add to this team," Atkins said.

Gregor Chisholm has covered the Blue Jays for MLB.com since 2011. Follow him on Twitter @gregorMLB and Facebook, and listen to his podcast.