Austin attended Dunbar High School in Baltimore, Maryland, where he played football, basketball and ran track. In football, he played running back, leading Dunbar High to three consecutive Class 1A state titles. As a senior, he had 2,660 yards rushing on 218 carries with 34 touchdowns, while also returning 12 punts for 446 yards and two scores. He was a Two-time Maryland Consensus Offensive Player of the Year and Consensus first team All-state. He set state records for career points (790), touchdowns (123), total offensive yards (9,258) and rushing yards (7,962). In track & field, Austin competed as a sprinter and jumper. He ran a career-best time of 11.43 seconds in the 100 meters at the 2009 1A North Region Meet. He was also a member of the Dunbar 400m relay squad.
Austin enrolled in West Virginia University, where he played for the West Virginia Mountaineers football team from 2009 to 2012. He was converted into a wide receiver as a freshman in 2009. During his freshman season he had 15 receptions for 151 yards with a touchdown and also rushed for 47 yards on six carries with a touchdown and scored a touchdown on a kick return. As a sophomore in 2010 he had 58 receptions for 787 yards and a team leading eight touchdowns. He also had 15 rushing attempts for 159 yards and a touchdown.
As a junior in 2011 Austin had 100 receptions for 1,180 yards and eight touchdowns. He added 189 rushing yards on 18 carries and another touchdown. He also returned two kicks for touchdowns. He was named a first team All-American by CBS. During the Mountaineers 70-33 win in the 2012 Orange Bowl, he set an Orange Bowl record with four touchdown receptions. He was the 2012 All-Purpose Performer of the Year as announced by the College Football Performance Awards association.
On June 13, 2013, Austin signed a 4-year, $12.751 million contract. The deal included a $7.653 million signing bonus. During his first year in the NFL, Austin played 13 games with 151 rushing yards, 418 receiving yards, and 678 return yards on 51 combined return opportunities during kick and punt returns.