Branch attended Cibola High School in Albuquerque, New Mexico. In addition to playing on the defensive line, Branch also played tight end as well as running back and punt returner in high school. He scored three rushing touchdowns and two receiving touchdowns in his senior season and five punt return touchdowns for his career. Branch was a fairly highly regarded recruit coming out of high school, ranked as high as #6 nationally among defensive tackles. Branch was also a three-year starter on the varsity basketball team, earning all-district honors as a sophomore and was second team all-state as a junior.
Branch, along with fellow defensive all-star LaMarr Woodley, anchored one of the best defenses in college football in 2006. He had 57 tackles, 17 tackles for loss, and nine sacks in 35 career games at Michigan. He had his first interception and a fumble recovery against Ohio State on November 18, 2006. Branch played both defensive tackle and defensive end at Michigan. He earned the following accolades while at Michigan:
The Seattle Seahawks signed Branch to a two-year contract on July 28, 2011.
Buffalo Bills
Branch signed a one-year contract with the Buffalo Bills on April 2, 2013. On December 23, 2013, Branch signed a multi-year contract extension with the Bills. On August 24, 2014, one day after being arrested for a DUI, Branch was cut from the team.
On October 21, 2014, it was reported that Branch had signed a 1-year deal with the New England Patriots. The team officially announced the signing on October 29. On February 1, 2015, Branch won his first Super Bowl, defeating his former team, the Seattle Seahawks, by a score of 28–24. On March 15, 2015, Branch re-signed with the Patriots on a two-year deal worth a maximum of $6.6 million. On November 21, 2016, Branch was notified that he was facing a four-game suspension for violating the league's policy on substance abuse but did not have to serve any games after the league rescinded the suspension before his appeal was even heard. Branch helped the Patriots win 14 games and earn the top seed for the AFC playoffs. On February 5, 2017, Branch was part of the Patriots team that won Super Bowl LI. In the game, the Patriots defeated the Atlanta Falcons by a score of 34–28 in overtime. The Patriots trailed 28–3 in the third quarter, but rallied all the way back to win the game, which featured the first overtime game in Super Bowl history and the largest comeback in the Super Bowl. Branch recorded three tackles, 0.5 sacks, and a crucial fumble recovery in the game. On March 9, 2017, Branch signed a two-year, $12 million contract extension with the Patriots. Branch played 12 games in the 2017 season and recorded 12 tackles. Branch was inactive for the playoffs, but the Patriots still made it to the Super Bowl without him only to fall to the Philadelphia Eagles in Super Bowl LII. On March 6, 2018, the Patriots declined the option on Branch's contract, making him a free agent in 2018.
