Ward-Smith ruptured his patella tendon and dislocated his knee in late January - just a week before his proposed England debut against Scotland - and was feared to have only a "borderline" chance of being involved in France.
But Knowles is a world authority on knee injuries having worked successfully on the likes of Richard Hill, Charlie Hodgson, Jason White and Austin Healey.
Ward-Smith said: "I'm really excited about the prospect of working with one of the world's foremost knee experts who will help me to get closer to my ultimate goal of playing rugby again."
"I'm incredibly grateful to both Bristol Rugby and the RFU for making this possible and hope to be able to repay them by making a full and speedy recovery."
Ward-Smith flies to the Vermont Orthopaedic Clinic in Killington Mountain Ski Resort tomorrow.
The goal is to progress his rehabilitation and establish a strong understanding of the training programmes that may be implemented when he returns to England.
Bristol's physio Paul Tomkins said: "Wardy has made great progress so far but Bill Knowles' reputation speaks for itself. This four-week period will be really important for Dan.
"He'll be in the best possible hands with Bill and I'm sure that Dan would agree that it'll be good to freshen things up with a change of scenery and a different group of people to work with for a while.
"Rugby is a team game and it's been a real team effort getting Dan this far. Through working together, we'll optimise his chances of making a full recovery as quickly as possible."