The 21-year-old agreed a loan deal at the DW Stadium until the end of the season on Tuesday, less than a month after moving to Fulham from Manchester United.
Tunnicliffe was signed by former Fulham head coach Rene Meulensteen but, with Felix Magath now in charge at Craven Cottage, he has been allowed to leave.
Rosler was keen to strengthen his midfield after Watson suffered a broken leg in last week's league clash against Barnsley, and believes that Tunnicliffe can bring something new to their play.
"Ryan is a promising young player who has experience in the Championship," the German told the club's official website.
"He is a very well educated footballer having come through the ranks at Manchester United and he will add a very good understanding of the game to our engine room in midfield.
"He has the potential to be a very good Premier League player and he will add an extra dimension to the way we play.
"He is a physical player with lots of energy and with the match programme we have coming up we needed to add another player who can play our style."
Tunnicliffe arrives at a Wigan side one point off the play-off places in the Championship and into the last eight of the FA Cup.
