The 30-year-old Cedeno is an eight-year major league veteran who hit .259 in 78 games with the Mets last season. He was in the Astros' starting lineup for Sunday's exhibition game against the Marlins.
Cedeno was released March 19 by the Cardinals, who opted to give him $188,525 in termination pay rather than keep his $1.15 million contract, which was not guaranteed.
Greene competed with Marwin Gonzalez for the starting shortstop position during spring training but hit .167 in 42 at-bats. The 29-year-old Greene would have to clear waivers before they can send him to the minors.
Houston also optioned outfielder J.D. Martinez to Triple-A Oklahoma City and reassigned catcher Jason Jaramillo to their minor league camp.