Callahan was released by the Giants in March, Baseball America reports.
Callahan (shoulder) signed a minor-league contract which includes an invitation to major-league spring training with the Giants on Friday, Bob Nightengale of USA Today reports.
Callahan (shoulder) elected to become a free agent after getting outrighted from the Mets' 40-man roster Friday, Tim Healey of Newsday reports.
Callahan will undergo shoulder surgery, Betsy Helfand of the Las Vegas Review-Journal reports.
Callahan was optioned to minor-league camp Tuesday, Matt Ehalt of The Bergen Record reports.
Callahan was called up by the Mets on Friday.
The Red Sox are trading Callahan, Stephen Nogosek and Gerson Bautista to the Mets for Addison Reed on Monday, Alex Speier of The Boston Globe reports.
Callahan has been promoted to Triple-A Pawtucket Christopher Smith of MassLive.com reports.
Callahan signed a minor league contract with the Red Sox that includes an invitation to spring training.