Jota and his brother Andre Silva were killed in a car crash in Spain on Wednesday evening.
With Liverpool and the city in mourning, Van Dijk posted to social media: "Man, I can’t believe it, I don’t wanna believe it. Absolutely devastated and in total disbelief.
"What a human being, what a player, but most importantly what an unbelievable family man.
"You meant so much to all of us and you always will! For your family to lose two sons, a husband and a father is just unimaginable. So cruel and unfair.
"My heart is breaking for all of your beautiful family, for Rute and for your kids. I promise you that in these difficult times and beyond we will always be there for your family.
"A champion forever, number 20 forever. It’s been a privilege to have stood by your side on the pitch, and to have been your friend off it.
"We will miss you beyond words and never forget you. Your legacy will live on, we will make sure of it!
"Rest in perfect peace Diogo & Andre."