The Astros on Monday said they were firing both manager A.J. Hinch and General Manager Jeff Luhnow for their roles in the scandal after Major League Baseball imposed one-year bans on each.
In its judgment on Monday, the league said Cora had arranged for the installation of a monitor showing centerfield camera shots, giving players the ability to decipher the signs and alert batters.
The Red Sox said it would not be possible for Cora to remain with the team given the league's findings.
"This is a sad day for us," Principal Owner John Henry, Chairman Tom Werner and CEO Sam Kennedy said in a statement.
"Alex is a special person and a beloved member of the Red Sox. We are grateful for his impact on our franchise." (Reporting By Amy Tennery; Editing by Peter Rutherford )