The council estimates that households with incomes ranging from just under £19,000 to £37,000 will benefit from the scheme, which is the first of its kind nationwide.
Mr Pickles said: ‘Our decision to raise discounts and extend eligibility under the right to buy has made homeownership a realistic option for London’s hard-working social tenants.
‘I’m delighted Hammersmith & Fulham will now go even further by offering shared ownership under right to buy, enabling more tenants to take their first step on the property ladder.’
The scheme is available to council tenants of three years or more, meaning they may be entitled to an element of the right to buy discount on the share they buy.
Hammersmith & Fulham plans to set the rent they pay on the remaining share at a level closer to social rents than market rents.
The scheme is being launched initially as a pilot, and the council will retain the discretion to buy back properties sold.
If the resident decides to sell, the property will be offered to the borough’s register of 6,000 local people hoping to secure a property.
Andrew Johnson, cabinet member for housing at Hammersmith & Fulham, said: ‘Right to buy part is something we’ve been developing for some time, and we’re confident it will enable more council tenants on modest or low incomes to realise their dream of owning their home by purchasing it, bit by bit, over a period of time that suits them.’
Inside Housing exclusively revealed the borough’s plans for the scheme in October.