The Dutchman, who has managed Ajax, Barcelona and Bayern Munich during his career, will replace David Moyes, who was sacked in April less than 10 months after being appointed as Sir Alex Ferguson's successor.
Last season, the Red Devils failed to qualify for the Champions League as they finished seventh in the Premier League.
"He's proved it at Barcelona, he's also proved it at Bayern Munich, so give him a chance," Gullit told Sky Sports News.
"It will be tough especially with the press. I can't wait for the press conferences with him. He's a character, he's a very good coach, knows how to prepare a team, knows how to do it and hopefully will do well with Manchester United. We're all going to follow him.
"He does everything himself, he wants to, but you have to accept the way he is. He is sometimes very confrontational, but if you win things why not take it?"