Leeds-born Mercer came through Bath's academy and developed a reputation as a skilful forward and a powerful ball-carrier, qualities that earned him two England caps in 2018.
However, the 23-year-old has elected to continue his career in the TOP14 with French giants Montpellier, with Bath signing Western Province and Stormers player Coetzee as a replacement.
"It has been a long-standing dream of mine to play in France," Mercer said on Bath's website. "The game is physical and will suit my playing style. I feel like I am able to offer the TOP14 something different.
"I've spent a huge part of my career with the Blue, Black and White and I will be forever grateful for the opportunities this has brought me.
"I found it impossible to say no to the offer of a long-term contract with Montpellier and I'm very grateful to have had respectful and honest conversations every step of the way with (director of rugby Stuart Hooper).
"There is a brilliant group of players and staff at Bath and I know they will go on to achieve great things together."
Coetzee, 24, has spent much of his career playing in his native South Africa, most recently with Super Rugby side the Stormers.
Hooper said: "Zach is an exceptional player and one who we feel very proud of. He has an exciting time ahead of him in France and after many conversations, we know this is the right move for him at this stage of his career.
"We will never hold any players back from realising their dreams and on this occasion, we see a brilliant young man leave to do just this.
"With Jaco's arrival, we feel we have an unbelievably exciting addition to the squad who will be available to play for the club for the full season.
"He's an intimidating ball carrier and will cause huge problems for our opposition no matter where he is on the field. I'm looking forward to seeing him compete with our current group of strong back rowers to get on the field for us."