A 6'8" forward, Early was a junior college star at Sullivan County Community College, where he was the two-time Division III NJCAAPlayer of the Year. After considering offers from major conference schools, he signed with Wichita State and coach Gregg Marshall. Early made an immediate impact for the Shockers, averaging 13.9 points and 5.4 rebounds per game. He was named first team All-Missouri Valley Conference and the MVC Newcomer of the Year. In the post-season, Early led the team to the 2013 Final Four in Atlanta. In the Shockers' semifinal game against eventual champion Louisville, Early scored 24 points and collected 10 rebounds in a narrow 72–68 loss. He was named to the All-Final Four team for his efforts. Going into his senior season, Early gained widespread national attention. He was named preseason Player of the Year for the Missouri Valley Conference and was named to the preseason top 50 watch lists for the John Wooden and Naismith Awards for national player of the year. Early helped lead the 2013–14 team to an undefeated 34-0 record entering the NCAA Tournament, becoming the first team in NCAA Division I men's basketball to do so in over two decades. Cleanthony put up an impressive effort in an attempt to help the Shockers advance to the sweet sixteen, with 31 points and 7 rebounds on 12/17 shooting. The Shockers ended up losing to Kentucky 78-76, ending their hopes of a final four repeat.
On June 26, 2014, Early was selected with the 34th overall pick in the 2014 NBA draft by the New York Knicks. On August 1, 2014, he signed with the Knicks. During his rookie season, he had multiple assignments with the Westchester Knicks of the NBA Development League. In three games for Westchester during the 2014–15 season, he averaged 20.3 points and 9.7 rebounds per game. On March 25, 2015, Early had a season-best game for New York with 18 points and 4 rebounds against the Los Angeles Clippers. During the 2015–16 season, Early has received multiple assignments to Westchester. On December 2, 2015, he became the fifth player ever to appear in both a Development League game and NBA game in the same day. On March 20, 2016, Early made his first appearance for New York since December 29, 2015, having been out for nearly three months with a knee injury he suffered after being shot on December 30. Early re-signed with the New York Knicks on October 18, 2016, but was waived three days later. On October 31, 2016, Early was acquired by the Westchester Knicks of the NBA Development League as an affiliate player of the New York Knicks.
On December 21, 2016, Early was acquired by the Santa Cruz Warriors in a three-team trade involving Westchester and the Texas Legends. In 16 games for Santa Cruz, he averaged 9.2 points and 3.9 rebounds per game. Early appeared in 19 games for Santa Cruz in the 2017–18 season.
On September 2, 2017, Early penned a contract with AEK Athens of the Greek League, but Early was stripped of his recently-signed contract with Greek club AEK due to disciplinary reasons on September 9.
In the early hours of December 30, 2015, Early was held up at gunpoint and shot in the right knee while traveling in an Uber. The attack took place after Early and his girlfriend left a strip club in Maspeth, Queens. He was taken to Elmhurst Hospital after the shooting where he was listed in stable condition.
