On 17 January 2018, Tavernier joined relegation-threatened EFL League One side Milton Keynes Dons on loan until the end of the 2017–18 season.[10] He made his debut for the club three days later in a 2–1 defeat to relegation rivals Northampton Town.[11] The club were subsequently relegated to the fourth tier of English football at the end of their unsuccessful campaign,[12] with Tavernier failing to score in any of his eight total appearances.[13]
In December 2017, Tavernier signed a new contract for 3+1⁄2 years.[14] In January 2020, this was extended until summer 2023.[15]
AFC Bournemouth
On 29 July 2022, Middlesbrough manager Chris Wilder confirmed that the club had accepted a bid for Tavernier from an unnamed Premier League club.[16] On 1 August 2022, Tavernier joined Bournemouth on a five-year deal.[17] Tavernier made his debut for the club on 6 August in a 2–0 home win over Aston Villa in the Premier League. He was praised by manager Scott Parker for his performance in the match.[18]