The 30-year-old is currently out of action after injuring his ankle playing for the Combined Nations All Stars against England last month.
Watson said: “It’s right for Aidan to move on.
“Aidan’s made his decision now. We spoke six or seven weeks ago about which way we wanted to go.
“Aidan’s made his decision now and I think that’s the best for him and the best for us now.”
Asked if he the former Canberra Raiders star is no longer at the club, the coach replied: “Yes, he’s doing his rehab.
“He won’t be involved in certain types of meetings now as he won’t be with us next year.
“For him, it’s about focusing on his own recovery now and his rehab.
“He’s had the operation. He was in the other day and is doing his recovery procedures with the physio staff and his conditioning work with the S and Cs to make sure he is in good condition for next year and when he goes to Leeds.
“But I just think for the group it’s important we focus on what we have and not what’s not here.”
Sydney-born Gavet, 31, was due to leave at the end of the season when his contract expired but he is departing early.
The Samoa international has been a regular since joining from Newcastle Knights at the end of the 2019 but was not included in a reduced 19-man squad for Friday’s visit of Hull FC.
Watson explained: “James is going to be going back home.
“That’s something he’s got to do. He feels it’s the right thing for him at this moment in time.
“He’s been brilliant. He’s been really up front with the club and really honest about the situation so we’ve known about this situation anyway.
“But he’s been a great pro’ in the meantime between the start of the season and him leaving.
“He’s been outstanding and putting his hand up every single week and playing to the best of his ability which is all we can ask for.”
Forward Owen Trout is back in the Giants squad as the depleted hosts seek to end a seven-game losing run and hooker James Cunningham could also return while Australian stand-off Jack Cogger is perhaps only one week away from his comeback from injury.
Meanwhile, with Sezer on his way to Rhinos, Gavet departing, Lee Gaskell confirmed as a Wakefield Trinity player for 2022 and Darnell McIntosh also leaving for Hull FC, it is understandable why some Giants fans are wondering who will be actually joining next term.
There has been no official news but Watson insisted: “We are far down the line (with reinforcements).
“Clubs like to announce them when the time feels right for them and when it’s also right for the players involved and the other clubs involved.
“That’s the way that Huddersfield explain it.
“Have we signed players for next year? Yes, we have.
“(But) the club wants to do it the right way and wants to fit for the other club as well.”