Artist's impression of the new Design Museum

London's iconic Commonwealth Institute will rise from the ashes - after plans were finally approved for the Design Museum to move there.

Following years of wrangling, including the threat of demolition, planning chiefs last night gave the green light for a massive redevelopment of the 1960s Holland Park building.

The famous "tent" roof will stay, with the main exhibition space remaining intact, and it will be renamed the Parabola.

But the admin wing will be demolished and three "cube"-like new buildings will house the Design Museum shop and cafe, plus 62 luxury flats which will help pay for the revamp.

The project, by Rem Koolhaas' practice OMA, is intended to "reconnect" with and rejuvenate the High Street Kensington area, bringing 400,000 visitors to the site each year.

Design Museum director Deyan Sudjic said: “We are thrilled. It opens the way for the Design Museum to realise its vision of becoming a world leading centre for design and architecture."

The project will cost the museum £7m, although the bulk has already been pledged from donors including Design Museum founder Terence Conran.

Construction begins in early 2011 with completion set for the start of 2013.

The Grade II* listed Institute was built in 1962, with a permanent exhibition about the Commonwealth nations. It has been left unoccupied since 2001, although squatters briefly moved in.

Its future had looked shaky, with the Government initially proposing to delist and demolish it before conducting a u-turn.

OMA's initial proposal was also rejected by Kensington & Chelsea council, but the proposed new buildings have been lowered in height and there will be fewer internal modifications to the existing structure.

Lord Cunliffe, part of the original team of architects who designed the Institute, said: "These proposals hearten me. They are in tune with the spirit of the building's creation."