He played college football for the Cincinnati Bearcats and Miami Hurricanes before being selected by the Chicago Bears in the sixth round of the 2014 NFL draft.

O'Donnell attended Palm Beach Central High School, and lettered three times in football and track for the Broncos.

[1] In high school, he averaged 45.1 yards on punts and also played kicker, having a 95 percent touchback rate when kicking off, along with making seven field goals as a senior.

[4] He made his debut with the Bearcats in 2009 as a true freshman against Southeast Missouri State, and appeared in three games before suffering an injury, causing O'Donnell to redshirt.

[3][6] In 2013, O'Donnell transferred to the University of Miami, citing interests to remain close to family, as his father was suffering from cancer.

O'Donnell recorded a school-record 47.1 punting average,[2] was named first-team all-ACC and the Hurricanes' Special Teams MVP at the end of the 2013 season.

[9] At the NFL Scouting Combine, O'Donnell recorded 23 repetitions on the bench press, better than 19 running backs, 21 defensive linemen (including number one draft pick Jadeveon Clowney),[2][12] and all 37 wide receivers invited.

[23] Later in the year, O'Donnell served as kickoff specialist against the San Francisco 49ers while kicker Cairo Santos was nursing a groin injury.

[27] Early in the 2019 season, O'Donnell served as kickoff specialist for the second time in Week 3 against the Washington Redskins with Eddy Piñeiro treating a knee injury.

[28] O'Donnell ended 2019 with a net punting average of 40.7 yards, setting the team record previously held by Adam Podlesh (40.4 in 2011).