The 5km extension would enable walkers and cyclists to access the Kilpatrick Hills.
This project will also provide an alternative route to the Balloch to Carbeth section of the John Muir Way, which runs along a public road and footpath.
Construction is due to start on the new path this week, with a scheduled completion date of May 2015.
Stuart Chalmers, District Forester, Forestry Commission Scotland, said: "This is a really exciting development for the John Muir Way. Our plan is to create this new link in Kilpatrick Hills which are an expansive hill range that tower above Dumbarton and Clydebank.
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"People enjoy visiting for the amazing views, sense of space, rugged beauty and wildlife. All of these qualities reflect what John Muir was all about, which is why we're delighted to be part of this project."
Louise Martin, Chair of sportscotland, added: "We are delighted to award £200,000 from the Active Places Fund and the Sports Facility Fund to this wonderful initiative that will take walkers and cyclists up to the Kilpatrick Hills and help them enjoy a wonderful part of the country.
"sportscotland is committed to providing more and better opportunities for people to take part in sport and physical activity and we view the John Muir Way as a key part of this commitment."
The John Muir Way opened in April 2014 as a new long distance walking and cycling route, offering visitors the chance to enjoy the landscape, nature and wildlife of central Scotland.
(JP/MH)
