Götze chested down a cross by Andre Schurrle, who had raced down the left-hand side past three Argentinians.
Götze's strike - a volley from close range which clinched the title in the 113th minute - was worthy of winning the tournament.
It will take a while for Lionel Messi, Gonzalo Higuain and Rodrigo Palacio to forget Sunday's heartbreaking defeat in Brazil.
They were all guilty of missing good chances to give Argentina the advantage.
Tens of thousands of Argentinians had flooded Rio hoping to see Messi inspire his team to their third World Cup win.
But it wasn't his night.
Despite his subdued performance during the final, the Argentinian captain was awarded FIFA's Golden Ball accolade after the match. It is given to the best player at the World Cup.
It was another fine performance by Germany goalkeeper Manuel Neuer, who was named Golden Glove for the tournament.
Colombia striker James Rodriguez picked up the Golden Boot award after he scored six goals during the tournament, while the Young Player Award was given to Paul Pogba of France.