The iron bridge over the Dighty Burn north of the town was built around 1796, and is thought to be the oldest surviving iron bridge in Scotland.
In 2012 it underwent significant restoration after a century of neglect and has become a popular feature for walkers and outdoor enthusiasts.
Mr Cordell said: “Everyone was really disappointed with the vandalism to the bridge earlier this year. The malicious and mindless damage to such an historic structure, that brings so much pleasure to those in the area, was really disheartening. Especially when we remember the long journey to bring the bridge back to its historic beauty.”
The A-listed bridge was re-opened in 2012 after a £400,000 facelift.
The refurbishment project involved developers Miller Homes, Scottish Heritage and Dundee City Council.
The current works will see the conservation of the existing balustrade, where salvageable, and carving and supply of new balustrading where the existing ornate stonework is beyond recovery.
Mr Cordell concluded: “This is £40,000 we would much rather not have to spend but the restoration of this bridge is so important both historically and for the aesthetics of the local area that I am delighted to see them brought forward."