The 22-year-old center-back played in all seven of Holland's matches as they secured third place at the World Cup finals in Brazil, and he scored his first goal for Oranje during the memorable 5-1 group-stage victory over Spain.
A tweet released by Lazio's official account on Wednesday evening read: "Lazio can confirm the permanent signing of Stefan de Vrij from Feyenoord."
The Krimpenerwaard native had been linked with a move to Manchester United, where he would have reunited with ex-Holland boss Louis van Gaal.
But it soon became clear that Lazio had won the race to secure his services when he arrived in Rome on Monday night in order to undergo medical examinations the following day.
De Vrij told Feyenoord's official website: "I didn't make my choice to join Lazio overnight. It is an informed decision which came about following many discussions with the club, where I had a good feeling.
"That good feeling has been reaffirmed over the recent days in which I have been completing the transfer.
"Lazio really proved that they wanted to have me and I am very happy I have made this move.
"I hope to become a more complete defender in Italy. I'll be playing against some world-class strikers, and that's a great challenge."
De Vrij has won 19 international caps in total since making his debut against Belgium in August 2012.
He is a product of Feyenoord's youth academy and made his first-team debut in 2009.
He follows midfielder Marco Parolo, striker Filip Djordjevic and full-back Dusan Basta in becoming a new recruit at the Stadio Olimpico as Lazio look to improve on the ninth-placed finish they achieved in the 2013-14 Serie A season.