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The 36 year-old has joined the Championship promotion-chaser for an undisclosed fee, ending his 10-and-a-half-year stay at Hillsborough.

Bannan, whose contract was due to expire at the end of this season, made 477 appearances for Wednesday after joining on a free transfer in August 2015, making him the sixth-highest appearance-maker in the club's history. He also netted 38 goals for the club across all competitions. 

This season, he leads the way for passes (1,689), successful passes (1,359), touches (2,129), interceptions (33) and possession won (150) for Wednesday in the Championship.

Bannan received a standing ovation from fans of both teams during his final match for the Owls, a 2-0 defeat at Bristol City.

Manager Henrik Pedersen announced Bannan wanted to leave after that loss, referencing the ongoing issues, including administration, which has Wednesday 20 points adrift at the bottom of the table with -7 points after 23 games.

"Millwall made an approach for Barry, and, with a heavy heart, he has decided it is an offer that he must accept and gives him the chance to fight for promotion to the Premier League," Wednesday said in a statement released on their website.

"Barry leaves Sheffield Wednesday as one of the club's modern greats, an inspirational leader on both sides of the white line.

"Through promotion pushes, relegation battles and periods of extreme difficulty, his commitment, professionalism and passion for Sheffield Wednesday have never wavered.

"He departs with the deepest respect and gratitude of everyone at Hillsborough, and we all hope he returns to Sheffield Wednesday in some capacity in the future."

Millwall is fourth in the Championship after a 4-0 thrashing of Charlton Athletic on Sunday, and just six points off the automatic promotion places.