The new contract, which covers the two years remaining on Cabrera's current deal and eight additional years, is expected to become official later this week, the source said.
According to CBSSports.com, which earlier reported Detroit and Cabrera were closing in on an agreement, the new deal also includes two additional vesting options worth $30 million apiece for years 11 and 12 that could bring the total of the deal to $352 million.
Multiple media outlets have reported that Cabrera needs to pass a physical exam before his new deal is complete.
If the new contract is calculated as a single, 10-year entity, it will surpass the 10-year, $275 million deal that Alex Rodriguez signed with the New York Yankees in December 2007, as the largest in Major League Baseball history.
Based on a career average of 607 at-bats per season and an average of $30 million annually, Cabrera would earn $49,423 per at-bat.
Cabrera, who turns 31 in April, is an eight-time All-Star in 11 seasons with the Marlins and Tigers. He's a .321 career hitter with 365 home runs.
He's the only major league player with 100 or more RBIs in each of the past 10 seasons, and last year he became the first Tiger to win three consecutive batting titles since Ty Cobb achieved the feat from 1917 to 1919.
Cabrera led the majors with a .348 batting average last year and his 44 homers and 137 RBIs were both second to Baltimore's Chris Davis.
The Venezuelan slugger won the Triple Crown in 2012 -- becoming the game's first player to lead either league in batting average, homers and RBIs since 1967.
The Tigers completed the extension with Cabrera just a few days after talks broke off on a long-term deal with pitcher Max Scherzer, the reigning AL Cy Young Award winner.
The Tigers said that Scherzer and his agent, Scott Boras, rejected a long-term offer that would have placed Scherzer among the highest-paid pitchers in the game.
Boras said it was the Tigers who took a pass on a multiyear offer from Scherzer.
Regardless of how the breakdown occurred, Scherzer's negotiations have been tabled. Barring a surprise, he will pitch for Detroit this season and hit the open market as a free agent in November.
Scherzer told the Detroit News on Thursday that he received an apology from Tigers president and general manager Dave Dombrowski about the way the contract talks had played out in the media.
"Dave and I had a meeting and a chance to talk," Scherzer told the paper. "He expressed regret over how things had been portrayed in the media. He said he needed to let fans know they [the Tigers] were doing their job. He regretted any negative light it might have placed on me. He also said he didn't give out any numbers and that he was upset over numbers that had been released."
Information from ESPN.com's Darren Rovell and The Associated Press was used in this report.