Defensive signings were always going to be high up on the agenda for O'Driscoll after he took charge at the City Ground and 31-year-old Welshman Collins brings plenty of experience to the back line.
Chairman Omar Al Hasawi said: "We are delighted to bring a player of Danny's experience and calibre to the club.
"We are sure he will prove to be an excellent addition to the squad Sean O'Driscoll is assembling for the challenges that lie ahead."
Portsmouth's Greg Halford is also being linked with a move to the City Ground. He is one of the seven senior players still on the books at Fratton Park who have been told they have the future of Pompey in their grasp if they cannot agree either a move away or come to a deal over outstanding wages.