Detroit received 18-year-old right-hander Wilkel Hernandez and 23-year-old outfielder Troy Montgomery in the trade.
The 35-year-old Kinsler hit a career-worst .236 with 22 home runs and 52 RBIs in 139 games last season for the rebuilding Tigers, who tied San Francisco for the worst record in the majors at 64-98. He is due to earn $11 million next season in the final year of his contract.
The four-time All-Star and 2016 Gold Glove winner adds a steady and productive veteran to the Angels lineup as they try to construct a playoff team around two-time American League MVP Mike Trout.
After going 80-82 last season to finish second in the AL West, Los Angeles recently landed two-way star Shohei Ohtani, who excelled as both a pitcher and hitter in Japan. Angels manager Mike Scioscia said the team plans to use Ohtani as a starting pitcher and a designated hitter.
With the Tigers shedding payroll, the Angels also acquired slugger Justin Upton from Detroit in an Aug. 31 trade and then signed the All-Star outfielder to a $106 million, five-year contract.
Upton solves a problem in left field for the Angels that has lasted years. Kinsler should be an upgrade at second base, where projected starter Danny Espinosa batted .162 with six homers in 77 games last year.
Los Angeles also made an Aug. 31 trade with Atlanta for veteran second baseman Brandon Phillips, who became a free agent this offseason.
Kinsler is a .273 career hitter with a .342 on-base percentage and .789 OPS. He has 234 homers and 839 RBIs to go with 225 stolen bases.
Kinsler was generally productive during four years with Detroit, although his batting average dipped to a career low in 2017. He was acquired from Texas in a trade for Prince Fielder and batted .275 with 78 home runs, 300 RBIs and 401 runs for the Tigers.
But the Tigers' run as a plausible contender ended with a thud last season, and they began looking toward the future, trading Upton, star pitcher Justin Verlander and slugging outfielder J.D. Martinez before September.
Hernandez has made 17 appearances and 12 starts, all at the rookie-ball level. He has gone 6-1 with a 2.28 ERA and is young enough that just about anything could happen with his career.
Montgomery hit .271 with eight homers and 38 RBIs in 100 games last season at Class A and Double-A.
Information from The Associated Press was used in this report.