The Yankees have also signed pitcher Kevin Millwood to a minor league contract, adding the veteran right-hander to the mix of candidates for the back end of their rotation, Major League Baseball's website (www.mlb.com) reported.
Dickerson, 28, has appeared in 173 games over three seasons with Cincinnati (2008-10) and Milwaukee (2010), compiling a .267 batting average in 454 at-bats with eight home runs and 35 runs batted in.
Right-hander Mitre, 30, was 0-3 with one save and a 3.33 earned run average in 27 appearances for New York last season.
Mitre had been a longshot to win a place in the Yankees' rotation this spring. In two seasons with the club he compiled a 3-6 record with a 5.03 ERA.
The 36-year-old Millwood, who had two 18-win seasons with the Atlanta Braves, was 4-16 last season in 31 starts for the Baltimore Orioles with an ERA of 5.10.
Ivan Nova looks to have won one of the last two spots in the Yankees' rotation with veterans Bartolo Colon and Freddy Garcia also in the competition.
(Reporting by Larry Fine, Editing by Steve Ginsburg)