The Bora-Hansgrohe rider had finished second on the stage behind Caleb Ewan (Lotto-Soudal), but replays show he used his head to push Van Aert out of the way and get past right before the line.
Sagan has been stripped of his second place finish and has been relegated to last place in the peloton because of the manoeuvre.
The official communication from the commissaires revealed that Sagan was penalised for “deviation from the chosen lane obstructing or endangering another runner and sprint.”
He was fined 500CHF (£421) and docked 13 points in the sprint classification.
The punishment means that Sam Bennett (Deceuninck – Quick-Step) is promoted to second-place finisher on the stage and extends his lead in the green jersey classification.
Bora-Hansgrohe said: “Peter Sagan has been relegated. We accept the jury decision. We always aim to win, but in a respectable way, even when the adrenaline is high in a Tour de France sprint finish.”
Deceuninck said on Twitter: “Green jersey wearer Sam Bennett moves up to second on the stage after Peter Sagan was relegated by the Tour de France commissaires.”
The stage was won by initially won Ewan ahead of Sagan and then Bennett, with Van Aert finishing third.
But after Sagan was penalised, Bennett claimed second with Van Aert bumped up into third.
The incident happened with just 50 metres left to the line, as Van Aert, Bennett and Ewan opened their sprints from the front.
Sagan was trapped between Van Aert and the right hand barrier, when he tried to move up alongside the Belgian.
He then put his head and shoulder onto Van Aert’s body and shoved him across to the left to make space, which enabled him to sprint past for second.
Van Aert then made a gesture towards Sagan after the finish to show his frustration.
Bennett continues to lead the sprint competition on 196 points, with Sagan still second on 175.