Oduba had always aimed for a career in sports broadcasting,[8] and initially joined The Network, an Edinburgh television festival scheme.
Oduba joined Newsround in August 2008, following the departure of Lizo Mzimba and Laura Jones.[6] His first role on the programme was as a reporter and breakfast bulletin presenter. He was quickly promoted to deputy presenter in 2009, filling in for main presenter Sonali Shah in her absence. In 2010, he joined Shah to begin presenting the main Newsround bulletin double-headed.[6] This continued until Shah's departure in November 2011. He was later joined by reporters Leah Gooding and Hayley Cutts. As part of his role he also presented spin-off show Sportsround. He became the main presenter in October 2008 when the show relaunched. He presented until its cancellation in 2010. The show was replaced by Match of the Day Kickabout which Oduba also presents. Oduba left Newsround in 2013.
Oduba formerly presented the sport for BBC Breakfast and BBC Radio 5 Live. He has also presented and reported on British Olympic Dreams along with former Newsround co-presenter Sonali Shah. Oduba began a debut presenting solo on the morning slot for the 2014 Commonwealth Games on BBC One and BBC Sport.[6]
On 2 March 2013, Oduba and Sonali Shah appeared on the BBC's Let's Dance for Comic Relief, dancing to Hey Ya! by Outkast. They were eliminated and did not get through to the final.[9]
He played the role of Nathan in Hacker Time on CBBC. Since 2015, he has guest presented numerous episodes of The One Show.
Between October 2012 and May 2017 he presented the daytime BBC One insurance fraud documentary programme Claimed and Shamed.[12] In November 2016, Oduba guest presented an episode of This Morning with Holly Willoughby on ITV. He returned to present a second episode with Willoughby in March 2017 and a third with Davina McCall in February 2018.
Oduba made his musical theatre debut in 2019, playing the role of Teen Angel in the UK tour of Grease.[6] He shared the role with singer Peter Andre. Following that, he starred as Aaron Fox in Kander and Ebb's Curtains alongside Jason Manford and Carley Stenson. The production later transferred to London's Wyndham's Theatre, where Oduba made his West End debut.[6]
In 2020, Oduba played the role of news anchor Akintola in the BBC One drama Noughts + Crosses, a television adaptation of the novels by author Malorie Blackman.[19]
In November 2015, Oduba married TV researcher Portia Jett Culmer, daughter of Nick "Animal" Culmer, lead singer of punk rock band Anti-Nowhere League.[20][21] They have two children.[22][23]
Oduba was the first winner of the Inspirational Public Figure Award at the inaugural Ethnicity Awards held in 2018. Other nominations included Meghan Markle, Chiwetel Ejiofor and Alesha Dixon.[27]