Newcastle Falcons' Gary Gold has already been confirmed as head coach at the Recreation Ground, and he has brought in the trio to work alongside Brad Davis.
More details about each of the coaches' specific roles will be provided when they report for pre-season in June.
"Bath is a great club, with clear goals and targets and know where they want to be," said Booth, who joins from London Irish.
"I'm really keen to start working with the squad. I have enjoyed all my coaching roles, but do feel now is the right time to move on to another club and challenge."
Former front row Hatley also arrives from the Exiles, while Mike Ford moves with Gold from Newcastle and has over nine years of international coaching experience with Ireland and England.
He has coached at three World Cups and also toured with the Lions in 2005.
"This is a fantastic opportunity to coach one of the most recognised club sides in the world," said Ford.
"Bath have great support from the most knowledgeable of fans, and I'm really looking forward to working with a strong coaching group and a great bunch of players."
Bath chief executive Nick Blofeld added: "This also demonstrates the club's long-term commitment to being the best we can be and getting the most out of a talented squad."
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