The south west outfit announced the signing on Monday, with the 28-year-old set to move to the English top flight from New South Wales Waratahs after the conclusion of the current Super 15 season.
The 27-year-old made his Waratahs' debut back in 2004 and has won more than 30 caps for the Australia national side.
He can also operate at flanker but prefers to do his work in the boiler room, and Baxter feels he has everything required to be a massive part of the club's future over the next couple of seasons.
"He's a very good signing for us and a very good player," he told reporters. "He is a back five forward coming into his physical prime.
"We've looked at lot at him and we believe he has got a lot of ingredients that we want him to bring to the club."
Exeter finished eight in their debut season in the Premiership but are currently fifth in the standings this season with just one regular-season game to go.
Victory over Northampton at the weekend would have guaranteed them a play-off berth but the 18-15 defeat means they must now win at Saracens to have any chance of making the top four.
Despite the disappointment, Baxter feels that it is testament to how far the club has come that top players now want to come and ply their trade in Devon.
"Personally, I think it's a great credit to what the players have achieved this season, and where we are as a club right now, that a guy of that standing wants to come and play his rugby here in Exeter," he added.