The two clubs agreed to a reported 10 million euro deal for the Dutchman on Friday, with the 24-year-old set to link up with his new teammates ahead of the 2013-14 season.
Van Wolfswinkel, who operates primarily as a striker, joined Sporting in 2011 from Eredivisie side Utrecht and has scored 14 goals this season after bagging 25 in the previous campaign.
"It has always been a dream of mine to play in England and in the Premier League, and I'm even more excited that I can hopefully fulfill that dream at such a great club like Norwich City," van Wolfswinkel told the club's official website. "Joining Norwich City is the perfect next step in my career. It's a realistic club with great people both at the club and in the city.
"I think this is the club for me and I hope to help them in every way I can. They have lots of ambition and I'll be delighted to be a part of that."
The Canaries look to be heading for Premier League safety again after winning promotion under Paul Lambert, and van Wolfswinkel believes they can push on with the guidance of current boss Chris Hughton.
"First of all, this is a club with great ambitions to become the team that they have been in the past in the top flight," van Wolfswinkel said. "The idea that I can be a part of that progress at the club, working with such great people, was enough for me to make what in the end was an easy decision. This is the sort of club I need at this moment in my career."