USA claim women's football gold after narrow victory over Brazil
Following a goalless first half, Swanson broke the deadlock 12 minutes after the break to earn the U.S. their first Olympic title since London 2012 after a perfect run in the tournament.
U.S. coach Emma Hayes enjoyed almost instant success as she secured the title only two months after taking the job.
"I'm very emotional, it's a dream of mine to be in this position," a tearful Hayes told Eurosport. "I have to thank my dad for pushing me to this point, to be able to come and coach an incredible group of players that have received me so well.
"(They have) taken on everything I asked, they are tremendous people, players and role models. I love them."
Brazil were dangerous in the opening stages and came close to scoring when Gabi Portilho drew a great save from Alyssa Naeher shortly before half-time. Naeher did well again in injury time to claw away Adriana's header from point-blank range.
Brazil great Marta returned after a two-match ban handed down for a red card, coming on as a substitute after the hour mark, but did not have much impact as Brazil were beaten by the Americans in an Olympic final for the third time.
Germany beat Spain 1-0 to win the bronze medal on Friday.
Swanson, making her 100th international appearance, found the net with a low finish after a solo run and a great pass from Korbin Albert to cut through the Brazilian backline.
It was her fourth goal of the tournament.
Brazil could not capitalise on the three big chances they created to send the match to extra time, but received a huge ovation from their fans after the final whistle.
It was an intense and evenly fought duel cheered by a huge crowd at Paris Saint-Germain's stadium, with the likes of American former Ballon d'Or winner Megan Rapinoe, ex-Arsenal manager Arsene Wenger and Tom Cruise also in attendance.
"The crowd was tremendous, Brazil was tremendous, I'm speechless," former Chelsea manager Hayes added.