Gregorius is presumably taking over the shortstop position from Yankees legend and future Hall of Famer Derek Jeter, who retired at the end of last season.
In his second season with the Diamondbacks in 2014, Gregorius, 24, hit six home runs and drove in 27 runs in 80 games.
Ray went 1-4 with an 8.16 ERA in six starts last season for Detroit after being acquired from the Washington Nationals in the December 2013 trade involving Doug Fister.
The 26-year-old Greene started 14 games this season for the Yankees and compiled a 5-4 record with a 3.68 ERA and 1.40 WHIP. He struck out 81 batters in 78.2 innings.
- Scooby Axson