Joseph, a member of England's elite player squad who won all four of his caps last year, will link up with former Exiles head coach Toby Booth at the Recreation Ground. The 21-year-old's departure is a blow to Irish, who were keen to retain one of the country's most promising young backs.
"I've loved my time with London Irish but feel it's time to make a move and Bath is an extremely exciting prospect," Joseph said.
"You can see what the coaches are looking to build there in terms of culture, they already have a really talented squad and I hope I can add something to that.
"Obviously I'm still developing as a player and I feel that Bath will give me a fantastic environment in which to do that."
Joseph's departure continues the exodus of big-name players from the Madejski Stadium with prop Alex Corbisiero also leaving at the end of the season, following in the footsteps of Delon and Steffon Armitage, Nick Kennedy, Paul Hodgson and Seilala Mapusua.
Bath head coach Gary Gold is delighted to have captured a player who would have been involved in the recent RBS 6 Nations but for injury.
"Jonathan is young, English and hugely talented. He is exactly the sort of player we want, and we are confident that he will indeed bring something special to the team," Gold said.
"That he has chosen Bath as his club says a huge amount about the environment we are establishing here. We can't wait for him to join the club."