With the two years left on his current deal and the eight additional years, Andrus would earn more than $131 million over 10 seasons.
The person spoke to The Associated Press on condition of anonymity because the deal won't be finalized until after a physical. That likely won't happen until Thursday, after the team wraps up its season-opening series at Houston. The Rangers play their home opener Friday.
The 24-year-old Andrus is already in his fifth major league season, and was part of the only two World Series appearances in Rangers history.
The new deal includes a vesting option for 2023. There is also the opportunity for Andrus to opt out and become a free agent after the 2018 season, not long after he turns 30 years old.
Andrus is already owed more than $11.2 million this season and next, the end of a three-year contract he signed before the 2012 season to take him through his final years being eligible for salary arbitration.
Andrus made his major league debut in the 2009 season opener after the Rangers moved five-time All-Star shortstop Michael Young to third base. At the time, Andrus was only 20 years old and had never played above the Double-A level.
In his 601 games the last four seasons, Andrus hit .275 with 123 stolen bases. Andrus went 0-for-4 with two strikeouts in the Rangers' season-opening 8-2 loss at Houston on Sunday night.
Second baseman Ian Kinsler got a new $75 million, five-year contract last season that locked up the three-time All-Star through 2017 and includes a club option for 2018.
Gold Glove-winning third baseman Adrian Beltre, another All-Star, is in the third year of his five-year deal with the Rangers.
Last season, Andrus hit a career-best .286 in 158 games. After his 25 errors in 2011 that were the second-highest total for a shortstop, Andrus had only 16 last season while playing 10 more games in the field.
Andrus was among several key players Texas acquired in July 2007 when Mark Teixeira was traded to Atlanta. The Rangers also got left-hander Matt Harrison, an 18-game winner and All-Star last season who started the opener Sunday night, and hard-throwing Neftali Feliz.
AP Sports Writer Ronald Blum contributed to this report.