The former Rangers assistant manager worked with Hart when he was a coach at Birmingham City in England.
The 60-year-old Scotsman has raved about the England international goalkeeper, and has backed the 33-year-old to be a success at the Glasgow giants.
According to The Daily Record, Celtic are interested in signing Hart in the summer transfer window, with the goalkeeper set to become a free agent after leaving Premier League club Burnley.
With Craig Gordon having left the Hoops this summer, the Glasgow giants do need to sign a replacement goalkeeper.
Watson told HeraldScotland about Hart: “He’ll still have so much to bring to the table. You don’t lose your ability, that doesn’t leave you, and he’s been at the very top level.
“Joe will want to do well, and he will want his back four to do well. He really buys into being part of the team.
“He’s not a loner, he knows the importance of the team, even though we’re going back a number of years now that I worked with him. He’ll be a good addition for Celtic or for any squad for that matter.”
Meanwhile, former Celtic star Kris Commons has criticised the Hoops for their decision regarding Gordon.
Gordon has left Celtic to return to Heart of Midlothian after failing to agree on a new deal with the Scottish Premiership giants.
According to The Scottish Sun, the Scotland international goalkeeper was open to staying at the Hoops, but the salary on offer was ‘vastly reduced’ than what he was on.
The Scottish Sun has quoted Commons as saying: “Celtic have made a major mistake in effectively forcing Craig Gordon out of the club. And, even if they now pull off a master stroke by landing Fraser Forster, they could pay a heavy price for this disastrous misjudgment.
“Would you put your hat on Scott Bain helping Celtic to ten in a row? Because it may come to that. I believe they’re getting close to signing Forster. But they should have made a bigger effort to hold on to Gordon.”