Shodipo was born in Leixlip, a town near Dublin, Ireland, before moving to London at the age of two. He signed a two-year contract extension with Queens Park Rangers in April 2016. He made his senior debut in the opening game of the 2016–17 EFL Championship season on 7 August 2016, in a 3–0 win over Leeds United at Loftus Road; he was named in the starting lineup, and was later substituted in the 68th minute for Abdenasser El Khayati. Manager Jimmy Floyd Hasselbaink later said that Shodipo had "that rawness... that streetness and that fight" and said "we will definitely be putting him in and around the team regularly". On 30 November, Shodipo signed a new two-and-a-half-year contract with QPR, tying him to the club until 2019. However new manager Ian Holloway left him out of the team in favour of new signing Kazenga LuaLua, explaining his decision by saying "every time I've put him on, unfortunately the team has let a goal in"; Holloway said "he would benefit massively from a loan spell", which he hoped would improve the defensive and tactical side of his game. On 30 January 2017, Shodipo signed with EFL League One side Port Vale on loan until the end of the 2016–17 season. He made six appearances for the "Valiants" before being ruled out for the rest of the season after picking up a tendinitis injury on international duty in March 2017. On 31 January 2018, he joined EFL League Two side Colchester United on loan until the end of the 2017–18 season. He came off the bench to make his debut on 10 March in the "U's" 1–1 draw at Mansfield Town. However he was limited to just two starts and four substitute appearances by manager John McGreal during his time at the Colchester Community Stadium. He suffered a significant tear to his thigh muscle in September 2018 and was ruled out of action for four months. He was praised by manager Steve McClaren upon his return to playing and featured four times for QPR during the 2018–19 season, before having his contract extended by a further 12 months in May 2019. Director of footballLes Ferdinand said that "He's had a tough time with injuries in the last couple of years but hopefully that is behind him now and we are looking forward to seeing him out on the pitch next season." He was handed a new contract by new manager Mark Warburton in September 2019, keeping him at the club until summer 2022.