Defender De Vrij memorably conceded a penalty for fouling Mauro Icardi on the last day of the 2017-18 season, an incident that directly contributed to Inter qualifying for the Champions League at Lazio's expense.
"It was destiny. All players are professionals, I don't think he fouled me on purpose," Inter captain Icardi said to Mediaset Premium. "He tried to stop me scoring, it was just destiny."
Inter have also completed the signing of Asamoah, the versatile Ghana international joining on a three-year deal from Juventus.
Asamoah had already announced he was moving from Juve to Inter and the Nerazzurri confirmed the deal on Monday.
Asamoah, who can play in defence or midfield, won four consecutive Coppa Italia titles and six successive Scudetti at Juve.