The creative duo, who have collaborated since they met at art school in 1967, will open the space in Heneage Street, in Spitalfields, on 1 April.
The Gilbert & George Centre will function as part of the pair's charity, with the aim of giving visitors the widest possible access to free art.
The duo said they wanted it to become a "leading cultural institution".
Gilbert & George appear as figures in their own art, known as 'living sculptures', and are recognised for their distinctive, suited appearance.
The centre has been converted from a former brewery and will host three galleries, with no admission charge for the majority of the programme.
The pair, from east London, said: "Our art is the friendship formed between the viewer and the pictures.
"We want our art to bring out the bigot from inside the liberal and conversely bring out the liberal from inside the bigot," they added.
The artists said their first exhibition would start with Paradisical Pictures, which shows the duo "wandering through natural worlds full of impressionistically-hued fruits, flowers, leaves and trees".
They added they envisaged the Spitalfields centre to become a leading cultural institution in London and a place for research and scholarship on the art of Gilbert & George.
It is anticipated the centre will host one or two exhibitions a year showcasing both historical and new pictures.