The new locations are in Bedfordshire, Cambridgeshire, Essex, Hertfordshire, Norfolk and Suffolk.
The company said those areas would join more than 1.2 million homes and businesses across the region which already have access.
Openreach said that it had plans to bring full fibre broadband to 517 more locations across the UK – covering a further 2.7 million premises.
"We plan to build even further across the region, to more cities and towns, and our most rural communities," said Kieran Wines, regional director for the East. "And our engineers, of which more than 3,500 live in the region, are doing this at a rapid pace - despite this being a hugely complex engineering project."
The towns and villages where the service will be rolled out are in:
Bedfordshire: Blunham, Hockliffe, Houghton Regis, Hexton, Ravensden and Toddington
Cambridgeshire: Burwell, Crafts Hill, Cheveley, Fowlmere, Harston, Melbourn, King’s Hedges - Cambridge, Steeple Morden, Sawston, Swavesey, West Wratting, Chatteris, Kimbolton, Newton, Parson Drove and Papworth St Agnes
Essex: Birch, Chafford, Earls Colne Fordham, Great Bardfield, Great Horkesley, Great Yeldham, Harlow, Marks Tey, Ongar, Purleigh, Ridgewell, Ramsey, Saffron Walden, Steeple Bumpstead and Tilbury
Hertfordshire: Barkway, Much Hadham, Puckeridge, Stanstead Abbots, Berkhamsted and Tring
Norfolk: Brancaster, Dickleburgh, Foulsham, Horning, Methwold, Pulham Market, Southrepps, Southery, Surlingham, Thursford and Tittleshall
Suffolk: Bacton, Bildeston, Barrow, Clare, Claydon, East Bergholt, Exning Grundisburgh, Holbrook, Kessingland, Nayland and Snape
The work is part of a £15 billion Openreach project to upgrade the UK's broadband infrastructure and make "gigabit-capable technology" available to 25 million homes and businesses by the end of 2026.
More than 4.7 million UK homes and businesses have already upgraded to full fibre.