The person spoke on condition of anonymity because no announcement had been made.
Fielder signed a $214 million, nine-year contract with the Tigers before the 2012 season that includes a limited no-trade provision, and the big first baseman was set to approve the deal.
Kinsler just finished the first season of a $75 million, five-year contract.
It's the first headline-grabbing move of baseball's off-season, and it involves two of the American League's top teams. Detroit has won three consecutive AL Central titles and reached the World Series in 2012, while Texas won the AL pennant in 2010 and 2011.
But neither team was about to stand pat. With stars like Fielder, Justin Verlander, Miguel Cabrera and Anibal Sanchez in the fold, Detroit's payroll had become one of the game's biggest. And although Fielder hit 55 home runs over the last two years for the Tigers, his numbers dipped this season and he struggled in the playoffs when Detroit lost to Boston in the AL championship series.
Fielder hit .279 with 25 homers this year, his lowest home run total over a full season. Kinsler batted .277 with 13 homers. He was limited to 136 games because of injuries to his ribs and right side.
The trade could give Detroit more financial flexibility, with Cy Young Award winner Max Scherzer a year from free agency.
Fielder, however, is still only 29, and the Rangers are set to add a big bat to the middle of their lineup while also resolving a logjam in the middle of their infield. Jurickson Profar, a highly touted 20-year-old prospect, appeared to be blocked by Kinsler and shortstop Elvis Andrus. Now, Profar should have a chance to play regularly.
The Tigers signed Fielder to a huge contract shortly before spring training in 2012 — after designated hitter Victor Martinez injured his knee. Martinez came back in 2013. With Fielder gone, Cabrera may move from third base back to first.
Kinsler fills a need at second base for Detroit after Omar Infante became a free agent.
Fielder is due $168 million through 2020, a salary of $24 million per season. Under his no-trade clause, he submits a list of 10 teams each year that he can be traded to without his approval.
Texas was not on that list this year, but Fielder agreed to accept the trade and instructed agent Scott Boras to approve the deal.
Kinsler is guaranteed $62 million through 2017: $16 million in each of the next two seasons, $14 million in 2016, $11 million in 2017 and a $5 million buyout of a $10 million option.
It's already been an unpredictable off-season for the Tigers. Manager Jim Leyland stepped down after the season and was replaced by Brad Ausmus. Detroit could have come back with a similar roster and probably been favoured to win the division again, but now more changes seem possible.
If Cabrera moves back to first base, prospect Nick Castellanos might replace him at third. Previously, it appeared Castellanos would have to play the outfield if both Cabrera and Fielder were still on the team.
Andy Dirks is still available to play left field, but that's a spot the Tigers could still try to upgrade. They also have six capable starting pitchers — Drew Smyly was used in the bullpen this year — so that's a surplus that could come in handy in a possible trade.
Detroit's bullpen will likely undergo a makeover after struggling last season.
The Rangers lost slugging outfielder Nelson Cruz to a late-season suspension as a result of MLB's investigation in the Biogenesis case. He's now a free agent, and if Texas loses him, Fielder should help replace his production.
Adrian Beltre and Alex Rios are among the dangerous hitters under contract next season in Texas. Beltre had an AL-high 199 hits and Rios, acquired from the Chicago White Sox in August after Cruz was suspended, has a year left on his deal.
The Rangers lost a one-game tiebreaker to Tampa Bay for the second AL wild card this year.
The trade agreement was first reported by CBSSports.com.
AP Sports Writer Ronald Blum in New York contributed to this report.