The revamped show will also be reduced from a weekly broadcast to a monthly hour-long episode.
Martha Kearney and Kirsty Wark will remain as presenters in a new primetime slot on the digital channel.
The Review Show has been one of the BBC's flagship arts programmes for nearly 20 years, and features contributors looking back at the week's cultural highlights.
The move has been criticised by various quarters, with Channel 4 News culture editor Matthew Cain tweeting: "Who's going to start a petition to save the BBC's Review Show? I want to sign it!"
It has also been described as a "typical piece of BBC cowardice" by Guardian writer Stephen Moss.
BBC Four controller Richard Klein defended the changes, saying: "The range of topics will be, I think, broader, but also we'll do what The Review Show does on BBC Two but in a number of different ways hopefully to expand audiences."
The BBC's arts commissioning editor Mark Bell said: "We feel that there are other ways of reflecting the arts topically beyond getting people to sit around a table and discuss it."
Arts coverage is being reduced across the BBC due to the £700m cost-cutting scheme Delivering Quality First (DQF).
Bell added: "On the whole I feel relieved. DQF is hitting all of us and arts has come out pretty well."