You just unplug the MR16s and plug in the LED equivalents, Wooders. That's the easy bit.
Transformers (properly called "drivers") can be a problem. It's a matter of trial and error. This week, I replaced nearly a hundred of them in a local pub. Only two of them flickered slightly, so the drivers will have to be changed as well. That can happen.
Sometimes, the old transformer can buzz. That's another possibility.
Purpose made drivers solve this problem, but adds to the cost.
No one likes 12v anymore - especially the LED suppliers. I would suggest stripping out the existing transformers and connecting 240v LEDs directly.
The only other expense is for the necessary fly-leads to connect them.