A roof garden and an inner courtyard have been opened to the public and plans are underway to green the remaining 3,000sq m of roof space.
Project manager Gavin McCourt said of the £300,000 project: "The garden roof had been leaking into the new galleries and into the costume store so we decided to reroof it to complement the gallery space. The roof shows what can be achieved with roof gardens."
The design features 80mm Sedum substrate-based planting along the top of the walkway at the museum's entrance and the roof garden houses a beehive as part of the City of London Festival.
McCourt added: "We have got greenery in the garden but some of the planting has been done to be bee-friendly." On greening the remaining roof space, he said: "It's been costed to the funding stage - we just need funding for the construction."
Dusty Gedge of livingroofs.org said: "We want to design the roof spaces so that they reflect the history of London."
The work was designed by Livingstone Eyre Associates and constructed by Woodpecker Joinery. Russell Trew oversaw the green roof installation and planting out was done by Calabasas.