The route will be partially closed from 19 January with traffic signals initially expected to be in place until 1 March.
Overnight works will see the road shut both ways for two to three hours each night in April.
Repairs will be carried out underneath the bridge and will not be visible to the public.
Emergency service vehicles are only allowed access during the closures.
Abnormally heavy vehicles that exceed normal legal limits will not be allowed to use the bridge. People cycling and walking will still be able to cross it.
Councillor Jon Andrews, Dorset Council’s cabinet member for place, said: “We understand these works will cause inconvenience, and we’re very sorry for that.
“If we don’t act now, the problems could become much worse and lead to longer closures in the future.”