"With record visitor numbers of over 110,000 people last year, the museum must evolve to offer the best possible experience for its visitors," said a spokesman at the museum, which celebrates its centenary this year.
That means creating new spaces for the museum's collections and library, a gallery, café and conference facilities, as well as a new entrance opposite Hoxton station to improve access. The aim is to open the redeveloped site in 2020.
Previous plans were thwarted following opposition to a proposal to demolish a disused former pub, The Marquis of Lansdowne. It will now be integrated within the overall design, and restored for use as a café or a shop.
The Geffrye, set in Grade I listed former almshouses surrounded by gardens, explores the homes of the British urban middle classes from 1600 to the present day, through a series of period living rooms.
Centenary celebrations include the exhibition Useful + beautiful: contemporary design for the home, which highlights the work of current designers and celebrates one of the museum's original purposes - to inspire the local furniture-making industry. It runs from April 29 until August 25.