The work, which also includes resurfacing, will take six weeks to complete and will require the bridge to be fully closed to traffic.
Highways Agency Project Manager Mark Arberry, said:
The current waterproofing is coming to the end of its life. Replacing it now and carrying out the bridge joint repairs reduces the need for future maintenance and the associated disruption to road users.
We would like to thank road users for their patience while we carry out this important work and advise drivers to plan their journeys and allow slightly extra time.
The A303 will continue to operate as normal but the A37 eastbound entry and exit slips will be closed for the duration of the works.
A fully signed diversion route will be in place advising driver wishing to join the A303 eastbound from the A37 to join the A303 westbound to Cartgate Roundabout, then turn around and continue along the A303 eastbound.
Traffic wishing to exit from the A303 eastbound carriageway on to the A37 will be diverted to continue along the eastbound carriageway to Podimore Roundabout, then turn around and travel back down the westbound carriageway to the A37 exit slip road.
Pedestrians will be able to cross the bridge throughout the works.
Members of the public should contact the Highways Agency Information Line on 0300 123 5000.
Journalists should contact the Highways Agency press office on 0844 693 1448 and use the menu to speak to the most appropriate press officer.