The Bayern Munich attacker started the match against the South Americans from the bench, but was brought on late in the second half to replace Miroslav Klose.
Gotze didn't let head coach Joachim Low down and found the net in the 113th minute after a cross from Andre Schurrle to fire Germany to their fourth World Cup title.
"It's an unbelievable feeling, I don't know how to describe it. I just took the shot and didn't know what was happening. It's unbelievable," the 21-year-old said.
"For us, the dream has become reality. I'm very proud of the team and extremely happy about everything that happened in Brazil.
"Every player in our team deserves to be mentioned here and we're very proud to have won this trophy."
Gotze made six appearances at the World Cup, scoring two goals in the process.