"It feels great to be back at the club where I experienced the best day of my career," McClaren told reporters on Friday.
"My last day here, 18 months ago, [when] we celebrated our championship with 80,000 fans, was the best ever."
After bringing the club their maiden title in May 2010 McClaren chose to move to Germany where he signed for Wolfsburg, but he was sacked in February 2011.
At the start of this season, the 50-year-old coach returned to his native England to coach Championship side Nottingham Forest, though he resigned after four months following a disappointing start to the season.
McClaren, replacing Co Adriaanse who was sacked by Twente earlier this week, said Dutch soccer had changed in his absence.
"My goal still is to compete for the title and to qualify for European football every year but not only are Twente ready to take the next step in their development, also the Dutch league has developed.
"Now there are five teams competing for the title and we are one of them."
Twente, who are third in the league, five points behind leaders AZ Alkmaar, have said there is no budget for new players.
"I need to talk with my staff and see some matches to see what is possible" said McClaren. "But so far the team has quality with several players I know but also some young, exciting players."
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