Brazil midfielder Luiz Gustavo insists he wants to play for Wolfsburg for many seasons to come.
Man City's Albert Rusnak hopes to stay at Cambuur until the end of the season but admits the decision is not his.
The Cottagers announced the move for the 32-year-old on their official website, saying they had paid an undisclosed fee for his services.
The announcement scuppered QPR's hopes of signing the player. Their boss Harry Redknapp was the man who took Parker to Spurs.
Parker makes a short hop across London in order to join Martin Jol's men, and Fulham are the fifth capital club he has played for.
"I'm delighted to be joining Fulham and I'm looking forward to meeting my new team-mates at training tomorrow morning," he said.
"Fulham is an established Premier League club and I look forward to trying to help the team progress even further over the next three years."
Parker started his career at Charlton, before moving to Chelsea. He then then headed to Newcastle, but returned 'home' for a successful spell with West Ham during which he was named as the Football Writers' Association Player of the Year.
United's relegation from the Premier League paved the way for Parker to move to Spurs, and it was while at White Hart Lane that he was asked to captain England in a friendly against Holland.
He started every group match at Euro 2012 and has made 18 England appearances, adding to in excess of 300 Premier League matches.
"I'm delighted that Scott has joined us," manager Martin Jol said.
"He's a midfielder who works tirelessly for his team and is a fantastic player both on and off the ball.
"It is wonderful to see a player of his stature playing for Fulham Football Club as he has shown his qualities in the Premier League and for the England team for many years.
"I'm happy that he's here and joins us for training ahead of our first home match of the season."