TFC have splashed out almost £20m to land Sargent.
The 26-year-old US international has signed a five-year contract with the Major League Soccer side after passing a medical.
Canaries boss Philippe Clement told BBC Radio Norfolk: "I wish I could have kept him. It's not the nicest and best situation, but finally there is an agreement. I wish him all the best. I really liked him as a player when we were working together.
"The club got a good price for a good striker, of course, as a manager you want to keep all your best players, but if there is the right amount of money for players we know that we are not in a situation to stop that.
"The good thing is there is clarity and money we can use in the summer to replace a striker with his quality. We need to move on and be happy for everybody."