The programme, on air in different formats for more than 20 years, is presented by Martha Kearney and Kirsty Wark and features a panel of commentators discussing cultural events.
Familiar faces on the show include novelist Ian Rankin and broadcaster Tony Parsons.
The move, which will inevitably spark accusations of dumbing down, was defended by BBC Four boss Richard Klein. He said the running time would be extended to an hour and it will occupy a primetime slot after going out at 11pm on BBC Two. It will also be repeated on BBC Two.
He said: “The range of topics will be broader but also we’ll do what The Review Show does on BBC Two in a number of different ways, hopefully to expand audiences.”
Mr Klein also announced a series of new arts programmes including documentaries about some of the country’s best-known artists and a look at the history of the National Theatre as it celebrates its 50th anniversary.
Among the programmes that will feature on the digital channel include An Evening with Joan Bakewell which will see Sir David Frost interview the broadcaster about her career.
There will also be documentaries about the jeweller to the Russian tsars, Peter Carl Fabergé, and the fairytale palaces built for King Ludwig II of Bavaria.
Mr Klein said: “Arts, music and culture have always served as the backbone of BBC Four but this year we’re increasing our commitment to topical arts, introducing new strands that will enable us to shine a light on contemporary arts, theatre, literature and film. ”