The 26-year-old defender has been heavily linked with a switch to San Siro for a number of months, meaning his involvement in the last-day drama between the sides in Serie A came at an unfortunate time.
With Lazio leading 2-1 and needing only a draw to qualify for the Champions League at Inter's expense, De Vrij fouled Mauro Icardi in the area and the Argentin striker converted the resulting penalty.
Lazio skipper Senad Lulic was then sent off before Matias Vecino's late header sealed a top-four spot for Inter.
Those now look set to be De Vrij's final acts in a Lazio shirt and he is relishing a new chapter in his career, even if his deal is yet to be confirmed by either club.
"I have signed for five years and I am really looking forward to it", De Vrij told reporters at Netherlands' training camp ahead of friendlies against Slovakia and Italy.
De Vrij joined Lazio from Feyenoord in 2014 and made 118 appearances for the Italian club, scoring 10 goals.