Kendricks was born in Milwaukee, Wisconsin. He attended Rufus King International Baccalaureate High School in Milwaukee, and played for the Rufus King Generals high school football team. In football, he was a two-time all-city selection, the Generals' most valuable player as a junior and senior, and the team captain as a senior. He caught 42 passes for 640 yards as a senior, and totaled 102 receptions for 1,905 yards during his high school career. He was also a member of the Generals basketball and track and field teams, and was a four-time AAU triple jump champion. At the high school track and field state championships, he finished third in the triple jump as a sophomore and second as a junior.
Kendricks attended the University of Wisconsin, where he played for the Wisconsin Badgers football team from 2007 to 2010. As a senior in 2010, he was a finalist for the John Mackey Award, received first-team All-Big Ten honors, and was recognized as a consensus first-team All-American. Prior to the 2011 NFL Draft, Kendricks was considered one of the top tight end prospects in the country.
Kendricks was selected 47th overall in the 2011 NFL Draft by the St. Louis Rams. On July 28, 2011, Kendricks signed a four-year $4.23 million contract with the Rams that included a $1.57 million signing bonus.