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Schweinsteiger, 31, spent 17 years with the current Bundesliga champions, winning eight league titles, the Champions League in 2013 and a FIFA Club World Cup, before joining United in July.
Injuries have marred Schweinsteiger's time in England and he has missed United's last seven games in all competitions with a knee problem, but Van Gaal said a consistent run in the side would allow him to get back to his best.
"I had to convince the board to buy him, because he's a very good player and he always gives a team more balance," the manager told the club's website.
"Manchester United has bought him even though he is now 31.
"Bastian has been unlucky because he picked up an injury at a time that he was playing very well – he was improving.
"He played very well at Wolfsburg and then began to reach the level he showed at Munich – I think he can (get back to that level)."
Fifth-placed United's 2-1 away defeat at relegation-threatened Sunderland in the Premier League on Saturday saw the gap widen to six points between United and fourth-placed Manchester City, currently in the last spot for Champions League qualification.
