As revealed by Goal in May, Colosimo makes the move to India, reuniting him with countryman and the club's coach Arthur Papas.
Papas and Colosimo were together at A-League club Heart in 2011, with the new Dempo coach welcoming the veteran defender's move.
"Simon is a player with a high level of experience in Australia, Europe and Asia, and internationally has represented Australia at all age levels, culminating in nearly 30 full senior appearances," Papas said.
"He has captained many of the teams he has played with and I expect him enhance our football style whilst imparting his knowledge, leadership and professionalism to assist our club in a time when we are undergoing a transition period.
"It is a coup for the club to have signed a player of Simon's calibre for next season."
It is the latest stop in a long career for former Socceroo Colosimo, 34, who has experience abroad with Manchester City [England], Antwerp [Belgium], Sivasspor [Turkey] and Pahang FA [Malaysia].
His clubs in Australia include South Melbourne, Carlton, Perth Glory, Sydney FC and Heart.Colosimo is expected to arrive in India in early July, having been released by Heart at the end of the 2012-13 season amid a host of squad changes.