Texas also signed right-handers Adrian Sampson and Rafael Montero to minor league contracts with invitations to major league spring training.
Farrell, the son of former big league manager John Farrell, went 3-4 with a 5.17 ERA in 20 appearances (two starts) for the Chicago Cubs last season before the Angels got him on a waiver claim Sept. 3. He never pitched for Los Angeles before being designated for assignment by the team last month.
Kansas City selected Farrell in the sixth round of the 2013 draft out of Northwestern. He has made 30 major league appearances the past two seasons with the Royals, Cincinnati and the Cubs.