The Netherlands international defender, who had been linked with Manchester United, will complete a reported €9 million (£7.1m) move to the Stadio Olimpico on Tuesday
The 22-year-old started all seven of Netherlands' games in Brazil this summer andhas now completed his move to the Italian club.
The centre-back completed his medical on Tuesday morning at the Paideia clinic, with Lazio's director of communications, Stefano Di Martino, describing De Vrij as "the best defender at the World Cup" and an "international signing".
De Vrij himself admits the decision to join the Serie A outfit required a great deal of thought but believes he will become a far better player in Italy's top flight.
"I had to think for a long time about the decision to choose Lazio," he told Feyenoord's official website.
"After a lot of talks with the people in Rome, Lazio gave me a superb feeling and now I have signed it feels only better. I am very happy with this step in my career.
"In Italy I hope to become a versatile defender. I will play against world class strikers. I am proud of being part of the Feyenoord family, but after many years here I am looking forward to the next challenge."
Lazio had been pipped to the signing of Cagliari's Davide Astori by city rivals Roma prior to bolstering their defence with the signing of the Feyenoord star.