The rats, whose ancestors were thought to have come ashore from shipwrecks in the 1900s, have been blamed for preying on seabirds on the Shiant Islands.
The islands, which are four miles (6km) off the coast of Lewis, provide habitat for more than 150,000 birds.
The Shiant Seabird Recovery Project is a partnership between RSPB Scotland, Scottish Natural Heritage and the Nicolson family, who have owned the Shiants for three generations.
Studies suggest that the rats eat seabird eggs and young chicks, harming the success of breeding seasons on the islands.
The islands support 10% of the UK's puffin population.
They are also home to 7% of the UK's razorbills.
The project's leaders say that poisoned bait will be used to eradicate the rats. The project will cost about £900,000 - Scottish Natural Heritage is providing £200,000 and the remainder will be raised from donations.
A project to wipe out non-native black rats from a group of small Scottish islands has been awarded almost £450,000 of European Union funding.