The Long Shelter has been a feature of the resort's seafront for nearly 100 years but was closed after becoming structurally unsafe.
The shelter will be replaced with a paved area made of pale sandstone that will include some seating.
Councillor Robert Whiting said: "It will cost us around £50,000 to carry out all the necessary work, but now we have got planning permission for the demolition and the replacement scheme, I hope that it will all be completed in time for the summer rush."
The rear wall which predates the shelter will also be renovated.
The shelter was built in the early part of the 20th century, with seven 3.5m arches, supported on six columns, running a total length of 28m.