The 24-year old former FC Utrecht and Vitesse Arnhem player is set to arrive at Carrow Road on July 1. Norwich did not disclose the transfer fee but media reports put a figure of £8 million on the deal.
"Ricky's profile is a perfect fit for us - he's young, ambitious and a proven goalscorer," Norwich manager Chris Hughton told the Norwich website.
"He has an excellent goalscoring pedigree and he's a young man very keen to continue his personal progression and to play in England. He's already an exciting talent but he still has more development as a player ahead of him.
"I'm delighted we've been able to agree a deal with Sporting Lisbon and with Ricky and we look forward to welcoming him to the squad in July, once all of the paperwork gets sorted out."
Van Wolfswinkel, who has become Sporting's top striker having joined for 5.1 million euros from Utrecht in June 2011, has played once for the Netherlands.
Sporting are enduring one of the worst periods in their history, languishing 10th in the league, and the Dutchman is their top scorer with eight goals in the championship.
With the club's presidential election looming this weekend, the prospect of selling Van Wolfswinkel has angered candidates.
"Sporting should not have to sell players to pay salaries. We cannot accept that," Bruno de Carvalho, the front-runner in the polls to be the next president, told o Jogo daily this week.
Van Wolfswinkel has scored a total of 14 goals in all competitions for Sporting this season after 25 last term. He bagged 35 goals in 80 appearances in two seasons at Utrecht.
The striker started his career with Vitesse Arnhem having joined them as a youngster in 1999. He made his senior debut in 2008 and scored eight goals in 35 games for the club.