Work on the £36m Chiltern Lifestyle Centre is set to start later next month with a target to open by the end of 2021.
The scheme includes an eight-lane 25-metre swimming pool, sports hall, dry diving training facility, squash courts and a library and community centre, among others.
The existing leisure facilities are over 50 years old and will be demolished. Amersham library has been temporarily re-located.
BAM’s Construction Director Mick Kelly said: “We’ll bring our expertise in creating leisure sector developments to this scheme that will transform the facilities for people here.”
Cllr Mike Stannard, Deputy Leader of Chiltern District Council; and Cabinet Member for Support Services, said: “After so many years of planning, it is fantastic that we are finally at the stage where work is starting on site. This is a major development and our priority is to ensure minimal impact on residents, pool users and staff while the work takes place.”