The Angels announced Rodney's signing on Thursday.
The 32-year-old Rodney saved 37 games in 38 opportunities for the Tigers last season. The Angels would be acquiring him primarily as a set-up man for closer Brian Fuentes. But the Angels are expected to give him some opportunities to close, as well.
Fuentes succeeded Francisco Rodriguez as the Angels' closer last season and led the league in saves, with 48. But he also had six blown saves and appeared to shake the confidence of manager Mike Scioscia during a second half in which Fuentes had a 4.81 ERA, a 1.685 WHIP and more walks (15) than strikeouts (12).
Rodney finished the season with a 4.40 ERA, the highest among AL relievers with 20 or more saves. But that figure was skewed by his 6.08 ERA in nonsave situations.
Because he was a Type B free agent and offered arbitration, the Tigers would get a supplementary draft pick as compensation.
Rodney led the league in save percentage and games finished, held opposing hitters to a .207 batting average and .366 slugging percentage with runners in scoring position, and had a 1.40 ground ball-to-fly ball ratio, which ranked first among free-agent closers.
Information from ESPNdeportes.com's Enrique Rojas and ESPN.com's Jayson Stark was used in this report.