In 2003, Travis played in the Little League World Series, representing Boynton Beach, Florida. They finished as the runner-up to the team from Tokyo, Japan. He attended Palm Beach Central High School in Wellington, Florida, and later Florida State University. In 2010, he played collegiate summer baseball with the Bourne Braves of the Cape Cod Baseball League.

On November 12, 2014, Travis was traded to the Toronto Blue Jays for outfielder Anthony Gose. In early 2015 he was named the sixth best second base prospect in baseball, as well as the number nine prospect in the Blue Jays’ organization by MLB. After a strong performance in spring training, Travis was announced as the Blue Jays’ starting second baseman on March 31, 2015. Travis debuted on April 6 and recorded his first career hit, a solo home run off Chasen Shreve of the New York Yankees. He also recorded two walks and scored two runs as the Blue Jays won 6–1. On April 12, Travis hit a three-run double to help the Blue Jays win 10–7 against the Baltimore Orioles. The hit was initially ruled an error on Travis Snider, however the call was changed on April 16, and Travis was credited with a hit and three RBIs.

Travis struggled to open the 2017 regular season, batting just .130 at the end of April. However, he would improve and bat .364 in May. In a 7–6 victory over the Texas Rangers on May 26, he hit the second grand slam of his career as well as his 15th double of the month. In doing so, he set the franchise record for extra-base hits in a month by a second baseman, tied Fred Lewis’s franchise record for doubles in the month of May, and became the first second baseman to hit more than one grand slam as a Blue Jay. On June 6, 2017, the Blue Jays placed Travis on the DL due to a bone bruise in his right knee. He subsequently underwent surgery in his knee and was expected to miss 3–4 months, but Travis wouldn’t return that season and finished the year playing in only 50 games.

On January 12, 2018, Travis signed a one-year, $1.45 million contract with the Blue Jays. In his first 18 games of 2018, Travis recorded a .148 batting average, one home run, and three RBI’s. On April 29, he was optioned to Triple-A Buffalo. He was recalled on May 22. Travis finished the season playing in 103 games, hitting .232 with 11 home runs and 44 RBI’s. Travis suffered left knee inflammation early in 2019 spring training, though an MRI revealed no structural damage. However, on March 13, he underwent arthroscopic knee surgery to repair a torn meniscus. Travis was outrighted off the Blue Jays roster on November 4, 2019, and elected free agency on November 7.