The 24-year-old, who has made 52 international appearances for Wales, will end a six-year spell with the Dragons.
Faletau, who has reached a World Cup quarter-final and semi-final in his career, will join Bath having won three Six Nations titles.
"The way Bath approach the game suits my style of play, which was a big factor in me wanting to join," Faletau told the club's official website. "The opportunity to work with Darren [Edwards] again after doing so with Wales Under-20 and the Dragons was also too good to turn down. I'd like to thank Dragons for everything they've done for me in my career."
Head coach Mike Ford added: "When we talk about this club being ambitious, we're not just paying lip service; signing a player of Toby's calibre is evidence of that. He is a world-class player who never takes a backwards step and he will add competition to an equally fantastic back-row. We're continuing to build a formidable squad that will challenge for silverware for years to come."
Faletau was also part of a British and Irish Lions Test series win over Australia.