The 22-year-old Puig defeated Germany's Angelique Kerber 6-4, 4-6, 6-1 in the gold medal match on Saturday, reports Efe.
Puig is the first Puerto Rican athlete to win an Olympic medal while representing the island.
"This is for Puerto Rico. This is definitely for them," Puig said after her victory on Saturday.
"They're going through some tough times right now, and they needed this. I needed this. I think I united a nation. I just love where I come from."
Puig, who is ranked 34th in the world, had never beaten the 28-year-old Kerber, who is the reigning Australian Open champion.
"I'm in shock, I just don't even really know what to say. I'm so excited."
The Puerto Rican player, who has won just one title in her professional career, had a magical run at the Rio Games, becoming the Caribbean island's first gold medalist.
"There's always a lot of jitters, a lot of anxiety there every single night. But I knew what was the main goal going in here, and I just can't believe it," said the women's singles gold medallist.
On her dream run to the gold in Rio, Puig knocked off Spanish world No. 4 Garbi?e Muguruza, the French Open champ, two-time Wimbledon champion Petra Kvitova, of the Czech Republic, Slovenia's Polona Hercog and Russia's Anastasia Pavlyuchenkova.
Kerber had not lost a set in the tournament, but Puig came out focused and played aggressively, refusing to let the German dictate the pace.
People gathered in bars and restaurants across Puerto Rico to watch the match, pouring into the streets and waving flags the second Puig sealed the win.
Automobiles clogged Ashford avenue, one of the busiest streets in San Juan, honking their horns in an explosion of joy over the island's first Olympic gold medal.
Puig's parents, Jose and Astrid, were unable to watch their daughter's historic win because they did not have enough time to obtain visas to travel to Brazil.
The two plan to fly to China next month to join their daughter in celebrating her 23rd birthday.
"The passports were being processed for visas for the China tour, which is when my birthday is," Puig added.
Gigi Fernandez, who was born in San Juan, won the gold in doubles at the 1992 Barcelona Games and the 1996 Atlanta Summer Olympics with Mary Joe Fernandez, but she played for the United States not the U.S. commonwealth.
Puig's gold medal gives people in Puerto Rico, which has been mired in a severe economic downturn for nearly a decade, something to celebrate.
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