The soldiers will be exercising their right to march through the city, after returning from a final Afghan tour.
They were the last group of British forces to leave Helmand Province earlier this year, when the UK's operations came to an end.
Prince Charles is Colonel in Chief of the regiment.
The Prince of Wales will inspect troops from the 1st Queen's Dragoon Guards  - the Welsh Cavalry - in Swansea next week, it has been announced.