The former England head coach had been interviewed for the vacancy at Blackburn Rovers, but has opted for the Dutch club, who are two qualifying games away from the Champions League group stage.
"It's an exciting time for the club, they were very successful under Fred Rutten and I cannot wait to meet the players and technical staff and to get to work.
"It's a great challenge for me to be with FC Twente in the Eredivisie and Champions League and I think we can all start with a positive feeling for the new season. I would like to say to the fans, about whom I have heard a lot, that we will do everything we can to bring the club further success."
McClaren had initially turned down the offer from Twente for family reasons, but, having resolved those concerns, has signed a two-year contract and will move to the Netherlands.
"Sir Bobby Robson told me that this would be a nice challenge for me," McClaren added. "He also told me that FC Twente is a fantastic club and that I would feel at home. I am excited to be working again at a club that fits me well. I am looking forward to this new challenge."