The 22-year-old was an ever-present for a Dutch side that finished third at the World Cup and raised his international profile with solid defensive performances and a goal against Spain in their opening match at the Brazil tournament.
He was due to undergo a medical on Tuesday, Lazio said on their twitter account (@officialsslazio), and was being offered a five-year contract.
Since making his Feyenoord debut in late 2009, De Vrij has played 135 times and scored seven goals. He has also earned 19 caps for the Netherlands.
Feyenoord, who play a Champions League qualifier against Besiktas on Wednesday, have already sold Graziano Pelle to Southampton, Bruno Martins Indi to Porto and Daryl Janmaat to Newcastle United in deals Dutch media claim to be worth 32 million euros for the Rotterdam club.