The scheme will be carried out in two phases, with work first taking place at the 68-space pay and display car park before moving onto the coach and lorry park.
Contractors Alliance Contracting Solutions will start on the pay and display site on Monday February 5 and the car park is expected to be closed for three weeks.
The contractors will then move onto the coach and lorry park which will be closed for two weeks.
Councillor Tony Kemp, High Peak Borough Council's Executive Councillor for Tourism and Regeneration, said: “While there is never a good time to close parking facilities we’ve chosen February, traditionally a quieter time of the year, and phased the works to minimise inconvenience for users of these facilities.
“Alternative car and coach parking is available at locations throughout the town and we’ll be putting up signage to direct drivers to the other sites.
"Unfortunately, there are no alternative sites for lorries in Buxton but we’re aiming to complete the work and re-open as quickly as possible.
“In the meantime I’d like to thank people for bearing with us whilst we carry out these essential maintenance works.”
Alternative car parking sites in Buxton include: Market Place, The Slopes, Buxton Town Hall; Spring Gardens, Wye Street; Pavilion Gardens, St John’s Road; South Street; and Bridge Street.
Parking for coaches is available on Burlington Road and at Pooles Cavern.