Burke played two years for the University of Michigan. In his freshman season, he was honored for the Freshmen of the Year of the Big 12 Conference. In his second year Burke led his university to the NCCA college finals, where they lost to the University of Louisville. Burke was honored for his services at the best players of his Conference. He was also honored as the best college player with the National Player of the Year Award and appointed to the NCAA All- Tournament team. His second year closed with 18.6 points Burke, 3.2 rebounds and 6.7 assists per game from.
In NBA Draft 2013 Burke was selected in the first round in 9th place of the Minnesota Timberwolves. Shortly after his selection Burke was transferred Jazz for the rights to Shabazz Muhammad and Gorgui Dieng to Utah.
During the preparation phase for the 2013-14 season, Burke suffered a broken finger and dropped in the first week of the new season of. On November 20, 2013, was, in the defeat against the New Orleans Pelicans, his debut and scored in 12 minutes operating time 11 points. In the win over the Orlando Magic on December 18, 2013 Burke scored a Karrierebestwert with 30 points. To this end, he distributed a further 8 assists and 7 rebounds fetched. Burke won the award for the Western Conference Rookie of the Month for December and was the first jazz players to have managed this since Karl Malone in 1985. He was also awarded for the month of January for the Western Conference Rookie of the Month. During NBA All-Star Weekend 2014 Burke took part in the Rising Star Challenge. He also took part, together with Damian Lillard at the NBA All-Star Weekend Skills Challenge and winning this.