He played college football for the Georgia Bulldogs and was selected by the Chicago Bears in the first round of the 2016 NFL draft.

Floyd attended Dodge County High School in Eastman, Georgia, where he played football and participated in track.

After high school, he attended Hargrave Military Academy for a year to take classes that met NCAA requirements.

[5] Floyd played in 11 games during his sophomore season, finishing the year with 55 tackles, six sacks, and a fumble recovery.

Coincidentally, teammate and fellow linebacker Jordan Jenkins also injured his hamstring and was unable to do the short shuttle and three-cone drill.

On March 16, 2016, he opted to participate at Georgia's pro day and ran drills for representatives from all 32 NFL teams, including head coaches Bill Belichick (New England Patriots), Rex Ryan (Buffalo Bills), Dan Quinn (Atlanta Falcons), and Todd Bowles (New York Jets) and general managers Thomas Dimitroff (Falcons) and Jerry Reese (New York Giants).

His vertical (35") was four inches shorter than his jump at the combine and Floyd was also unable to do the bench press due to a pectoral injury.

[16] He competed with Pernell McPhee, Lamarr Houston, Willie Young, and Sam Acho throughout training camp for a job as the starting outside linebacker.

[17] He made his professional regular season debut and first career start in the Bears' season-opener against the Houston Texans and recorded six combined tackles and was credited with a half a sack on Brock Osweiler during their 23–14 loss.

[24] On December 24, 2016, Floyd made one solo tackle, but left the Bears' 41–21 loss to the Washington Redskins after suffering a concussion.

[28] Floyd competed for the starting outside linebacker job throughout training camp against Pernell McPhee, Lamarr Houston, and Willie Young.

[29] On September 28, 2017, Floyd recorded three solo tackles and sacked Packers' quarterback Aaron Rodgers in the Bears' 35–14 loss.

[31] On November 19, 2017, he earned five solo tackles before being carted off the field after sustaining a leg injury after he collided with teammate Kyle Fuller in the Bears 27–24 loss to the Lions.

On November 23, 2017, the Bears placed him on injured reserve for the remainder of the season after he suffered a sprained MCL and PCL in his right knee.

[46] In Week 7 against his former team, the Bears, on Monday Night Football, Floyd recorded two sacks on Nick Foles during the 24–10 win.

[51][52] In the Wild Card Round of the playoffs against the Seahawks, Floyd sacked Russell Wilson two times during the 30–20 win.

[60] In his lone season with Buffalo, he finished with 10.5 sacks, 32 total tackles (21 solo), one pass defended, and one forced fumble in 17 games and 16 starts.