Jansen was released from his Ewood Park contract at his own request having failed to re-establish himself at Rovers following a motorcycle accident in the summer of 2002.
Allardyce said of Jansens arrival, "Matt has great potential, even though he hasn't been involved with Blackburn of late and I do believe he has the right qualities to resurrect his career here at The Reebok."
Meanwhile, Bolton along with many other clubs have been alerted to Wanye Bridge's availability.
Chelsea are ready to send Bridge away on-loan and Spurs, Fulham and Newcastle are among the clubs scrambling to sign the England left-back, 25, until the end of the season.
With his side 13 points clear at the top of the Premiership, Blues boss Jose Mourinho has had a change of heart after first refusing Bridge's plea for a temporary move.