The project, one of four to receive funding today from the BLF as part of a move to ensure all of its new grant programmes in England support local communities, encourages citizens to play a more active role in their local areas.
Other recipients of the £5.76m awarded by the BLF as part of its launch of People-Powered Change are: The Young Foundation, which has received £820,000; UnLtd for its Big Venture Challenge, which has received £2.2m; and Nesta's Neighbourhood Challenge, which was given £2m.
Twivy co-founded the charity Big Society Network with Lord Nat Wei, the government's big society adviser, in early 2010. He has since stepped down as its chief executive and runs Your Square Mile.
A statement from the BLF said the project would use the funding to develop a digital platform to support its pilot and subsequent roll-out.
"The locally controlled digital platform will aggregate community activity providing people with access to local information and resources, including information about local groups, opportunities and local support services," it said.
"Your Square Mile has already embarked on 16 pilots and will launch the first stage of its digital platform in late summer. It will then launch as a mutual for all citizens to join in the autumn."