All three players' deals were due to expire in the summer, but an additional one-year option has been activated in all three respective contracts.
Over the course of the current season Pukki has netted ten goals in in 31 appearances. Since signing for City as a free agent in the summer of 2018 the Finland international has registered 77 goals in 161 appearances in all competitions.
Bournemouth retain an option to make the deal permanent at the end of the current season.
Young midfielder Dennis has spent the current season on loan with National League side Southend. He has scored eight goals in 28 outings for the Shrimpers.