The Brewers need to cover several starts while 2009 AL Cy Young winner Zack Greinke recovers from a broken rib.
"Sergio, he's going to be in a good spot to, obviously, help Milwaukee with their recent rash of injuries," Yankees general manager Brian Cashman said.
The 30-year-old Mitre is 13-29 with a 5.27 ERA in seven seasons with the Cubs, Marlins and the Yankees. He is 1-1 with a 5.73 ERA in 11 innings this spring training.
Dickerson gives the Yankees backup insurance if center fielder Curtis Granderson, out with a strained muscle on his right side, is not ready for opening day next Thursday.
The 28-year-old Dickerson was acquired by the Brewers from Cincinnati last August for Jim Edmonds. He's hitting .278 with five RBI in 17 games in spring training, but was expected to lose out for one of the last bench spots to Brandon Boggs and Jeremy Reed.
"It gives us another choice as an alternative if Curtis doesn't make opening day," Cashman said. "We're not going to treat opening day as a pressure point. I don't think it's a long-term issue, but I can't tell you whether it's a few days or a week or 10 days."
Granderson did light running and agility work on Friday, but did not swing a bat. Yankees manager Joe Girardi said Granderson's status can't be fully determined until after he resumes hitting.
"It's a little clearer, for sure," Girardi said. "We talked about three of the four guys going [with the team for opening day] and now you take one away. Could things change? Yes, they could. But we've said all along that it would be, probably, three out of the four."
Garcia and Nova appear ready to claim the starting roles. If not in the rotation, Colon could replace Mitre as the long reliever.
"We still have more time there," Cashman said. "I can't tell you if we're going to give you the white puff of smoke today."
The Yankees also reached agreement on a minor league deal with Kevin Millwood. The 36-year-old righty was 4-16 with a 5.10 ERA last season with Baltimore, where his 3.26 runs per game of support was among the lowest in the majors.
Millwood is 159-137 with a 4.11 ERA in 14 big league seasons. He will work out at the Yankees' spring training complex until joining Triple-A Scranton/Wilkes-Barre.
Yankees backup C Francisco Cervelli (broken left foot) is scheduled to stop using a protective boot for the injury on Tuesday.