The Brazil captain held his nerve after the scores were tied 1-1 at the end of extra-time in a pulsating final at the Maracana stadium, Xinhua news agency reported.
Lars Bender was the only player to miss in the shoot-out, with Brazil goalkeeper Weverton punching away the midfielder's feeble attempt.
FC Barcelona forward Neymar had earlier opened the scoring with a superb first-half free-kick but Germany equalised through a 59th-minute strike from captain Max Meyer.
Brazil's victory came barely two years after they crashed out of the World Cup on home soil with a 1-7 thrashing against Germany in Belo Horizonte, a result that was described by the country's media as a national tragedy.
An Olympic Games triumph had been the only major prize to elude the five-time World Cup winners and their bid for gold in Rio had become something of an obsession.
Brazil had previously reached the final on three occasions -- 1984, 1988 and 2012 -- but had to settle for silver each time.
The Olympic football tournament doesn't quite have the prestige of the World Cup, but Brazilian fans have embraced it in a way that other Olympic sports can only envy.
While many events during these Games have been played out in front of empty stands, the Selecao has mostly enjoyed near-capacity crowds at their matches. That was again the case on Saturday, with 78,000 braving the rain to fill the Maracana.
After starting the Olympic tournament with two goalless draws, Brazil won their next three matches by an aggregate of 12 goals.
Germany's form had been even more impressive, with 21 goals for the tournament, including six each from SC Freiburg striker Nils Petersen and Arsenal midfielder Serge Gnabry.
Perhaps understandably, Brazil began nervously as a settled-looking Germany took control of possession. The visitors nearly went a goal up in the 10th minute when Julian Brandt's dipping long-range shot cannoned off the crossbar.
The close call seemed to spring the hosts into action.
Luan's shot after a Douglas Santos cross was cleared off the line and Renato Augusto volleyed wide from a corner.
Neymar then sent the Maracana into a frenzy when his curling free-kick rebounded in off the under side of the bar. It was a goal of the highest quality and prompted wild celebrations in the stands.
Brandt continued to pose a threat for Germany, particularly from set pieces. He almost engineered an equalizer when his sumptuous free-kick was headed just over the bar by Bender.
The visitors continued to press and finally broke through just before the hour after opening up Brazil's defence with some slick passing.
Jeremy Toljan found space on the right and whipped a cross into Meyer, whose first time effort flew beyond the outstretched arms of goalkeeper Weverton.
Urged on by their fans, Brazil attacked in waves in their attempt to break the deadlock.
Renato blasted just wide from distance and new Manchester City signing Gabriel Jesus also narrowly missed with a close-range volley.
Neymar almost lifted the roof off the stadium when he jinked past an opponent and lobbed a shot wide of the post.
Luan had a golden chance to score the winner in the sixth minute of extra time but dithered in the area and failed to get a clear shot away. Brandt then volleyed over for Germany as play pinballed from end to end.
Second-half substitute Felipe Anderson nearly ended the impasse for Brazil just after the extra-time interval when he was played in by Neymar and forced a smart save from Horn. But Germany defended resolutely to force the match into a penalty shoot-out.
