The signing, confirmed by a person familiar with negotiations but not authorized to speak publicly about them, is not expected to be announced until Smith passes a physical.
Smith, who turns 30 in March, has been one of the American League's most durable and dependable relievers for the last three seasons, compiling a 16-9 record and 2.42 earned-run average in 197 innings over 213 appearances.
The right-hander relies primarily on a hard sinker and slider delivered out of a sidearm motion designed to produce more groundouts than strikeouts. Because the Indians did not make a $14.1-million qualifying offer to Smith, the Angels will not relinquish a draft pick to sign him.
Smith should provide depth to a bullpen that ranked 26th in baseball with a 4.12 ERA and converted 41 of 58 save opportunities in 2013. If veteran left-hander Sean Burnett recovers from elbow surgery, Manager Mike Scioscia will have two solid setup options in front of closer Ernesto Frieri.
With Friday’s acquisition of third baseman David Freese and Saturday’s addition of Smith, Angels General Manager Jerry Dipoto will devote his full attention to the team’s most pressing need -- the acquisition of at least one and probably two starting pitchers.