Fly-half Ford was capped at Under-18 and Under-20 level before making his England Saxons debut this season and has made 38 first-team appearances for Tigers, scoring 263 points.
Scrum-half Young has also played at Saxons level and moves to The Recreation Ground after 17 appearances in two years with Leicester.
Bath head coach Gary Gold said: “George is an exceptionally talented young player, and we are very much looking forward to him joining us. He has already shown a tremendous range of skills and at just 19 we know he will only grow as a player and further develop those skills.”
After announcing the signing of Young and fellow scrum-half Martin Roberts, Gold added: "Micky and Martin are both very strong, capable players with good core skills and the ability to do things the opposition don't expect. They are still young, and we are looking forward to having them join the squad here and seeing them develop further."