In a statement, Bath said that Faletau will be departing the Recreation Ground “for an unnamed Welsh side”.
But the PA news agency understands that the back-row forward is to join Cardiff with an announcement expected by the Arms Park region later this week.
Faletau, who has won 86 caps and played in five British and Irish Lions Tests, is now with the Wales squad preparing for remaining Autumn Nations Series games against South Africa, Fiji and Australia.
He has not played so far this season due to an ankle injury, but would have been unavailable for Wales’ 54-16 defeat against New Zealand on Saturday.
That game fell outside World Rugby’s autumn international window, with English clubs not releasing Welsh players for such fixtures.
Faletau will become the latest high-profile capture for Cardiff after they signed fly-half Rhys Priestland from Bath earlier this year, while Wasps flanker Thomas Young is also on his way to the Arms Park next summer.
Bath said: “The number eight has his sights set on the 2023 World Cup and will return to the Welsh region in order to put himself in the best possible position to perform for his country.”
And Faletau added: “I will leave Bath at the end of the season with fond memories, both professionally and personally, plus two Bath-born sons.
“Bath has been a brilliant club for me over the years and I owe it a lot.
“I will miss the team and everyone at the club, but my heart is set on returning to Wales and hopefully continuing my international playing ambitions. It feels like the right time for me and my family to return home.”
Bath rugby director Stuart Hooper said: “It continues to be a privilege to work with Taulupe. He is a world-class number eight who makes a significant impact on the field.
“As we develop our squad for 2022, a crucial factor is the availability of our players throughout the season.
“Having a squad that can compete during the international calendar is becoming fundamental as the quality of competition in the Premiership increases.
“Taulupe leaves with our blessing and we all wish him well for his future.”
Hooper said the coronavirus pandemic has changed the rugby landscape and the growing crossover between club and international fixtures was a major factor in Faletau’s end-of-season departure.
“When we started building this squad three years ago the world was moving to a point where we were going to have very limited crossovers between the club and international calendar,” Hooper said.
“By next season we were getting to the point where there was only going to be one or two games that crossed over. The reality is that Covid hit and that changed the landscape.
“If you’re an England player you miss 13 games, which is massive, and the quality of the Premiership is there for everyone to see.
“Taulupe is a fantastic player and we’ll miss him. But there is an element that we strategically focus our resource where we can and have people available for the whole year which is massively important.”
Hooper, however, suggested that Bath would still sign international players in the future.
He said: “It’s about the context of the position, the other people you have in that position, the nationality of players, the games you are likely to play.
“You can’t put a blanket across it and say you don’t want to sign internationals.
“Internationals are still a huge part, and a valuable part, of what we do but there has to be a balance.”