Solarte was added to the 40-man roster before the Yankees opened the season at Houston on Tuesday night.
The team also placed infielder Brendan Ryan on the 15-day disabled list with a cervical spine nerve injury, a move retroactive to March 22.
General manager Brian Cashman said it was a difficult decision to let Nunez go.
''It was less to do with Eduardo and more to do with what Dean Anna and Salarte showed this spring,'' he said. ''We were fortunate to have everybody come to into spring training on the infield side and do very well. It put a wrinkle in our decision-making process. These guys provided us choices so we made those choices.''
Nunez, who was New York's opening day shortstop a year ago with Derek Jeter out, hit .260 in 90 games for the Yankees last season. He was signed as an free agent in 2004 and played parts of four seasons with the team after his debut in 2010.
His played in a career-high 112 games in 2011 and hit .265 with five home runs and 30 RBIs.
The Yankees now have 10 days to trade him, release him or send him outright him to the minor leagues.
''He possesses a great deal of talent and you could dream on him as a potential everyday shortstop in the big leagues,'' Cashman said. ''All that talent is still there and I think his versatility will provide for a great deal of choices once he ends up as a player on a major league roster. So we'll see what develops over the next 10 days.''
Manager Joe Girardi said Nunez was a victim of a ''roster crunch.''
''I've said all along it's someone we've that we've been very fond of and (is) a great guy in the clubhouse,'' he said. ''It's tough.''