Van Gaal worked with Schweinsteiger when the pair were at Bayern Munich between 2009 and 2011.
The German has now joined Man United on a three-year contract worth around £130,000-a-week.
Van Gaal praised Schweinsteiger and insisted he will be a quality addition at Old Trafford.
Speaking about the transfer, van Gaal said: ”Bastian is, of course, no stranger to me. I worked with him during my time at Bayern Munich and I am truly delighted he is joining Manchester United. His record speaks for itself; he has won every honour at club level and was a major part of the successful Germany World Cup-winning team last summer.
“Bastian is the ultimate professional and there is no doubting his talent and his ability to control games. He brings a wealth of experience and is an excellent addition to our squad.”
Schweinsteiger has won practically everything there is to win with Bayern and the national side and his signing is a major coup for United.
It is a testament to the player’s character that he wants to challenge himself at Old Trafford rather than winding his career down in Germany. Excitement surrounding him has reached fever pitch and it is safe to say that supporters cannot wait for the new Premier League season to begin in August.