Roberts was named to the All-MEAC second-team in 2012 and finished 11th for the Jerry Rice Award, given to the nation's top freshman on the FCS level.

[8] As a senior, Roberts was a team captain and made 142 total tackles, which was good enough to lead the American Athletic Conference and place him fourth in the nation.

Multiple scouts stated they were impressed with his power, mobility, and his performance in positional drills supervised by Houston Texans defensive coordinator Mike Vrabel.

[16][17] Head coach Bill Belichick named Roberts the backup middle linebacker to begin the regular season, behind Dont'a Hightower.

[18] He made his first NFL start on October 16 against the Cincinnati Bengals and tied for second-highest tackles on the team with seven in the win.

[5][19] In Week 16 against the New York Jets, Roberts led the team with 11 tackles, including a forced fumble recovered by Malcolm Butler.

[26] Roberts helped the Patriots reach Super Bowl LII, but they lost 41–33 to the Philadelphia Eagles; he recorded six tackles in the game.

[28] The Patriots reached Super Bowl LIII after defeating both the Los Angeles Chargers and the Kansas City Chiefs in the playoffs.

[31] In 2019, Roberts was voted a team defensive captain for the first time, replacing safety Patrick Chung.

[32] He was a member of the team's high-performing linebacker corps, and nicknamed "The Boogeymen" by teammate Dont'a Hightower.

Starting in Week 7, he began to play on offense as well as defense, where he was primarily used as a fullback after injuries to teammates James Develin and Jakob Johnson.

His older brother, Eli Roberts, graduated from Sam Houston State University with a major in Criminal Justice.