Andrus is due to make $4.8 million this year and $6.48 million next year before the new eight-year deal kicks in. The extension gives Andrus the option of opting out after four years and includes an unspecified vesting option for a ninth season, sources confirmed to ESPNDallas.com.
Rangers general manager Jon Daniels previously declined to comment to ESPNDallas.com on the talks that led to the agreement, the specifics of which were earlier reported by FoxSports.com.
Andrus underwent a physical Monday, and the Rangers are expected to officially announce the new contract by the end of the week, sources told ESPNDallas.com.
The Rangers have locked down another key member of their infield with Andrus, second baseman Ian Kinsler and third baseman Adrian Beltre all under the club's control through 2016. Kinsler signed a five-year, $75 million contract extension last April.
Andrus batted .286 with three home runs and 62 RBIs in 2012. He helped the Rangers make their first two World Series appearances in 2010 and '11. He has a career .275 average and 123 stolen bases in his four seasons as the Rangers' starting shortstop.
The 24-year-old began his fifth season with the Rangers on Sunday night, going 0-for-4 with two strikeouts in the team's 8-2 season-opening loss to the Houston Astros.
In February, Andrus said his agent, Scott Boras, had talked with the Rangers about the possibility of a long-term deal.
"I want to be here," Andrus said at the time. "I love it here."
Andrus was asked during spring training whether he'd consider getting a deal from the Rangers now rather than wait.
"It's a lot of different things [to consider]," he said. "A lot of those guys are married and they have kids. For me, it's a little different. I'm still super young, and I have no wife, no kids. I'm going to continue to play and let things flow."
Information from ESPNDallas.com's Todd Wills and Richard Durrett was used in this report.