Tatupu began his career in rugby league with Australian outfit Melbourne Storm before switiching codes and representing Super Rugby franchise Western Force and NPC for Otago.
"I'm really excited about this move and cannot wait to get over to Exeter," said Tatupu, who has been capped by Samoa at both league and union level. "
I've been over and had a good look at the set-up, which is great, and I had a decent chat with Rob about the direction of the club.
"I'll be honest I didn't know too much about Exeter before the move, but I know they've had a great season this year and that they are looking to build on that for next season."
Welcoming Tatupu to Sandy Park, Baxter said: "We are really pleased to have Josh on board, he's a guy we have been watching for quite a while now. Obviously it has taken time to get him over from France to meet us and do all the necessary tests, but once we got that done everything has moved pretty quickly and we believe he is going to be a very good, long-term addition to the club.
"He is a good age at 24, so it's the right time for him to move here; he's got a lot of assets that modern backs need - he's strong, very quick and has an interesting background having played both rugby league and union - but now he has settled on the union path and he has been putting in some very good performance for Castres.
"He can play centre or on the wing, so he kind of fits very nicely in what we have here. We've got quite a few guys who can play multiple positions and I think Josh coming here will give us a real amount of strength right across our back line."
Baxter added: "He's been playing in the Top 14 this season, which is a tough division, and other than a short period when he was injured with a broken cheekbone, he's been playing regularly for Castres in a tough competition. As I said, he's got good pace, good hands, good vision, good defender - all the things you need when you are playing tough Premiership games.