The Olympic champion, racing his first season as Classics leader for Ag2r-Citroën, wasn’t able to follow the decisive move as Kasper Asgreen, Mathieu van der Poel, and Wout Van Aert broke free of their rivals on the Oude Kwaremont.
But Van Avermaet, 35, rode a patient race in the second group on the road, eventually attacking with one other rider and sprinting to a strong third-place.
Speaking after the finish Van Avermaet, who has longed dreamed of winning the Tour of Flanders, said: “This was the best result achievable.
“I wasn’t among the best, certainly not among the best three. “I knew from experience that I had to stay in the chasing group and that I could compete for the podium.
“I am very pleased that I am still on the podium in the Ronde.”
Van Avermaet has been fighting to win his home Monument, having already won Paris-Roubaix, E3 Harelbeke, Ghent-Wevelgem and Omloop Het Nieuwsblad.
The Belgian has now finished on the podium four times, having said last year he is running out of chances to win the race.
After this year’s edition, he added: “It was a fast pace from the Molenberg and certainly not easy. I had hoped to be just a little better, but felt that I was not enough. I was good in the chase, but I didn’t have the punch to follow the big men at those moments.”
Victory went to Deceuninck – Quick-Step’s Kasper Asgreen who, after launching a decisive attack which established an elite trio out front, took a surprise win by out-printing Mathieu van der Poel (Alpecin-Fenix) in the final.