The Reds reluctantly released Troisi from the remainder of his contract on Monday, just two weeks out from the start of the A-League campaign.
"I've known Carl since 2015 when he tried to sign me at Vancouver, we've kept in touch and we have a very close relationship," Troisi said in a statement.
"Carl is a fantastic person and we've seen in a short time already what he is able to do in this league.
"I am coming to the club to be successful and I want to win another title with this club.
"The ambition of the club is high, from everyone I have spoken to, and it's something I want to be involved in."
Troisi joined Adelaide on a two-year deal last October and made 13 A-League appearances for the Reds last season.
However, he didn't feature when the league resumed after the coronavirus break due to knee surgery.