The Rural Payments Agency (RPA) is providing £4m for the work - the bulk of which will be carried out within the Lake District National Park.
Cumbria and the north of England were left with a clean-up bill of more than £500m after last December's storm.
The government says £150m has already been spent aiding flood-hit areas.
The RPA said £3m of the grant would be used in the national park - which saw £5.8m of damage to footpaths and bridges.
Floods Minister Thérèse Coffey said: "This new £4m fund will mean visitors and residents can continue to enjoy all parts of the Lake District.
"We remain committed to continuing to help the people and businesses of Cumbria recover from the devastating winter floods."
Richard Leafe, chief executive of the Lake District National Park, said: "This year we've made a start on repairing some of the areas most affected by the floods, but with limited funding from our own resources and donations, it's been a challenge.
"This £3m will allow us to launch our extensive recovery programme that will not only reconnect flood-damaged public rights of ways, but also make them more robust and resilient for the future.
RPA chief executive Mark Grimshaw added: "The Cumbrian countryside, including the Lake District National Parks, includes some of the most beautiful scenery that England has to offer and is a major feature of the local tourist economy.
"This will help restore rights of way popular with locals and visitors as well as protect them from any future instances of flooding."
The remaining £1m will be shared between local councils and the Canal and River Trust.
Millions of pounds is to be spent repairing paths and trails across Cumbria that were damaged by flooding from Storm Desmond.