The trade agreement was first reported by CBSSports.com.
Tigers general manager Dave Dombrowski called his counterpart in Texas, Jon Daniels, Tuesday morning and floated the idea of trading Fielder for Kinsler.
"Dave called yesterday and threw out the concept," Daniels said. "We had a little dialogue before on it. From there, David and I had a series of phone calls and both sides were interested and we got the money where both sides could live with it."
It was made official Wednesday evening. As part of the deal, the Tigers are sending $30 million to Texas to offset Fielder's cost, senior baseball analyst Keith Law confirmed. Fielder had to approve the deal and did.
Fielder still has $168 million due to him over the next seven seasons, so Texas will pay him $138 million over that period.
Kinsler is guaranteed $62 million over the next four seasons, which includes a $5 million buyout on his 2018 club option. In total, Detroit will pay $92 million in the deal -- $62 million to Kinsler and $30 million to Texas for Fielder.
The Tigers were not among the teams on Kinsler's no-trade list.
Fielder, 29, hit .279 with 25 homers and 106 RBIs in 2013, his second season in Detroit. He gives the Rangers a power-hitting, left-handed hitter for the middle of their lineup, something Daniels listed as the top priority heading into the offseason.
"He fits what we're looking for -- a middle-of-the-order power threat that is durable and plays to win," Daniels said. "He's a good complement with Adrian Beltre in the middle of our order."
Daniels added that Fielder will be the primary first baseman and that the club is still figuring out Mitch Moreland's role.
The Tigers get a three-time All-Star second baseman and someone who has hit in various parts of the lineup. Kinsler, 31, batted .277 with 13 homers and 72 RBIs last season.
The Rangers can put highly-touted prospect Jurickson Profar at second base in Kinsler's place, relieving the logjam at middle infield.
It's the first headline-grabbing move of baseball's offseason, 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, 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.
The trade could give Detroit more financial flexibility, with Cy Young Award winner Max Scherzer a season away from free agency.
Daniels acknowledged that Fielder is coming off a season in which many of his offensive numbers were the worst of his career. But the general manager added that the Rangers likely couldn't make the deal if Fielder had played as well as he had in the past.
Fielder's batting average (.279), home runs (25), OPS (.819) and slugging percentage (.457) were all down from 2012. The slugging, OPS and homers were the lowest of his career.
Still, Fielder has been durable -- at least 157 games in each of his eight full seasons -- and despite the drop in his numbers last season, is still very productive and brings a big bat to the Rangers' lineup.
"If anybody feels like that's a sign of things to come that he's slipping, you may not like the deal," Daniels said. "We don't feel that way. We're excited by what we see of him in the future."
As for where Fielder will bat, manager Ron Washington hasn't decided that yet. He did say he wants to leave Beltre at the cleanup spot.
Washington said he is excited to write Fielder's name on the lineup card next season.
"He has presence," Washington said. "He's been a very productive player. He's a winning player. I do believe he'll fit well in this clubhouse."
Information from The Associated Press and senior baseball analyst Keith Law was used in this report.