The company said that nine towns and villages across the county would be able to access the service.
Elstead, Farnham, Tadworth, Ashtead, Camberley, Ottershaw, Puttenham, Upper Warlingham and Worplesdon will all receive access by December 2026 "if not sooner", the firm said.
The investment is part of a £15 billion project to upgrade the UK's broadband infrastructure to enable full fibre broadband access to some of the "hardest to reach and most rural parts of the UK".
Openreach plans to bring full fibre services to 2.7 million homes and businesses across 517 additional locations by 2026.
Kieran Wines, Openreach's regional director for the South East, described the rollout as "a huge infrastructure success story".
He said: "Our fibre checker has the latest information about our work in your area, but only 36 per cent of premises in Surrey which can order a new ultrafast service have done so, as upgrades aren’t automatic.
"Once full fibre is available where you live, you’ll need to place an order with a provider of your choice to get connected and we’ll do the rest."