The former technology and property investor, now specialising in urban regeneration, based in Edinburgh and listed on the Alternative Investment market, said it had agreed terms to acquire a first London site for its private rented sector (PRS) residential portfolio.
The site is within the 443-acre Barking Riverside development in east London, which is one of the largest residential regeneration schemes in the UK and in Europe.
Sigma's planned 318 new homes, a high proportion of them for families, would have a £50 million development cost.
Barking Riverside has planning permission for 10,800 new mixed tenure homes and chief executive Graham Barnet said he was "hopeful this won't be the only phase we get involved in".
Sigma said it expects to "acquire further sites in Greater London, the South East and elsewhere in the UK", and Mr Barnet confirmed that he is "very keen to explore possibilities in Scotland".
Sigma's breakthrough in the sector won formal endorsement from Prime Minister David Cameron when it was announced three months ago and yesterday London's mayor Boris Johnson welcomed "Sigma's innovative purpose-built private rental housing model".
The Scottish company will sign a contract with Barking Riverside, a joint venture between Greater London Authority and housebuilder Bellway by May 31.
It expects site construction to begin in late 2014, subject to site acquisition agreements and funding arrangements, and to be completed in 24 months.
Sigma has worked with Bellway in Solihull and at Winchburgh in West Lothian, where it is managing the biggest development of its kind in Scotland for Sir Tom Hunter's West Coast Capital.
Ted Ayres, chief executive of Bellway Homes, said he was pleased to be working with Sigma in London.
Mr Barnet, who owns around 20% of Sigma, said: "Barking Riverside is one of the largest and most ambitious development projects in the UK and we are delighted to be playing a small part in its delivery with such prestigious partners."
It follows November's announcement of Sigma's joint venture with Gatehouse, a Shariah-compliant investment bank, for a proposed £700m development of up to 6600 new rental homes for a PRS residential portfolio, utilizing Sigma's existing local authority partnerships in north-west England.
Bank funding for the initial roll-out of around 2000 new homes in Greater Manchester and Liverpool is said to be "currently under negotiation".
Mr Barnet said Gatehouse was "the obvious partner" for the London project, adding: "They are extremely keen on it, but it would be fair to say there is a lot of interest from at least five other funders as well."
That might enable Sigma to build its portfolio more quickly. "The whole idea is to create a repeatable model.....there is more in the pipeline."
Sigma's shares, barely 6p a year ago, rose 3p to 67p yesterday, following their 60% leap to 40p in November.
They are still only halfway to recovering their 2000 flotation price, but Mr Barnet has noted that current shareholders led by Henderson, AXA and Victory Asset Management bought in at low levels.