In 2007, Andrus joined the Myrtle Beach Pelicans of the Carolina League. During the season, he was selected to the All-Star Futures Game and was selected again for the showcase in 2008.

On July 31, 2007, Andrus, Jarrod Saltalamacchia and three minor league pitchers (Matt Harrison, Neftalí Feliz and Beau Jones) were traded from the Braves to the Rangers for Mark Teixeira and Ron Mahay.

With Rangers shortstop Michael Young agreeing to move to third base in 2009, Andrus earned the starting job on Opening Day. He was the second-youngest player in the American League at the time. As Andrus was only 20 years old, Texas signed veteran shortstop Omar Vizquel for insurance.

Andrus stole his 20th base on July 28, 2009, in his rookie season. Andrus was the 10th player in major league history to steal 20 bases under the age of 21. The last player to do that was then-teammate Andruw Jones in 1997 with the Atlanta Braves. Andrus was named to the 2010 American League All-Star team as a reserve shortstop.

Andrus’ older brother Erold Andrus played in the independent leagues in 2009 and 2010 as an outfielder. He has played in the organizations of several MLB teams. During spring training of 2011, though Erold was in minor league camp, he got the opportunity to play in a Rangers spring training game, the first time that Erold and Elvis played together in the United States.

In 2010, he batted .265, without any home runs. He led the AL in sacrifice hits (17), was 2nd in caught stealing (15), and 9th in stolen bases (32).

In 2011, Andrus batted .279, with 5 home runs. He was 3rd in the American League in sacrifice hits (16), 4th in caught stealing (12), and 5th in stolen bases (37). On defense, he led all AL shortstops in errors, with 25, and was 2nd among league shortstops in putouts (245) and 3rd in assists (407). In 2012, Andrus earned his second All-Star selection, batting .286 while leading the American League in sacrifice hits with 17.

Andrus is a Christian. In 2012, Andrus donated $12,500 to OurCalling, a Christian charity that helps homeless people in Dallas County.

Two of Andrus’ brothers remain in Venezuela. Andrus voiced concern about his home country during civil unrest in early 2014. “As a human being, you always get angry when you see what’s happening with the military back home doing stuff to the civils, and to the students, and that’s what really gets me angry. I’m not a political guy, but I just hate when you see somebody just walking and trying to say something get hit by police, or get hit by any military from the country that’s supposed to defend the country instead of shoot him or hit him”, he said.

Andrus finished 2015 with career lows in batting average (.258), OBP (.309), and sacrifice hits, while posting a career-best seven home runs and stealing 25 bags for the AL West champion Rangers. On defense, he led the major leagues in assists, with 516. He batted .182 in the Rangers’ ALDS series against Toronto and made two of the team’s three errors in the pivotal seventh inning of Game 5, won by the Blue Jays. In 2016, hit .302 with eight home runs and 69 RBIs.

He continued the following season, in 2017, to post a career offensive season, hitting .297 with 20 home runs and 88 RBIs and 25 steals in 158 games. On defense, he led the major leagues in assists, with 490.

Andrus married girlfriend Cori Febles in a ceremony at his home on June 1, 2017. The couple welcomed their first child, Elvis Emilio, on July 6, 2017. On November 28, 2018 they welcomed their second child, a girl, named Lucia Alessandra. For the 2019 season, Andrus adopted “Baby Shark” as his walk-up song because it reminded him of his children.

On April 11, 2018, Andrus was hit by a pitch on his right arm and left the game. X-rays and CT scans tested positive that Andrus had suffered a fractured right elbow. As a result, he was placed on the disabled list for the first time of his Major League career. No surgery was required, but to keep out of baseball activity for 6-8 weeks. He was activated on June 18 from the disabled list. Andrus finished 2018 hitting .256/.308/.367/.675 with 6 home runs and 33 RBI.

Andrus hit .275/.313/.393/.707 with 12 home runs, 72 RBIs, and 31 stolen bases in 2019. He tied for the AL lead with 10 sacrifice flies.

On July 26, 2019, Andrus became a naturalized US citizen.

In 2020, Andrus batted .194/.252/.330 with three home runs and seven RBIs in 103 at bats, and his .969 fielding percentage that was his lowest in 10 seasons.