The Holland international has moved to the Serie A side from Feyenoord on undisclosed terms.
The 22-year-old, who played in all seven of Holland's matches as they secured third place at the World Cup finals in Brazil, has revealed several clubs were interested in securing his services.
But former Dutch and now Manchester United boss Louis van Gaal did not make a bid for a reunion at Old Trafford.
Speaking at his official unveiling, he told a press conference: "I am very happy to be here in a big club and in a big city.
"Lazio were the only club that showed a real interest in me before the World Cup.
"After the World Cup, I evaluated other options but I received the best feelings from Lazio and I'm happy to be here.
"Several clubs contacted me, I don't think it's fair to say the names. I can say that Manchester United were not one of them."
When asked if he would welcome Aston Villa's centre-back Ron Vlaar joining him at Lazio, he added: "I have played with him since we were 17-years-old, he is a great player and a friend of mine.
"But the choice is up to the president."