The south-west outfit will ply their trade in England's top division next season after topping the Greene King IPA Championship table.
It will not be a low-key return to the top flight as, for the second time in 20 years, the Ashton Gate outfit will have a new name.
They previously became Bristol Shoguns as part of a sponsorship deal and owner Steve Lansdown explained the reasons behind the decision, as they had to be "prepared to break the mould".
"This is an exciting and major commitment to ensuring the future success of the club," he added. "We recognise that there is a history and tradition associated with all sports clubs and we are conscious and proud of the loyalty, bond and passion so many share for Bristol Rugby."
Head coach Pat Lam said he "loved the idea" of a name change to the Bears when first consulted.