The Swiss rowers fought off Denmark, bronze medallists in London four years ago, who went one better to land silver, and the French quartet who claimed bronze.
Speaking to Swiss daily 20 Minutes, Tramèr, from Geneva, said he was “incredibly proud” of the team's achievement but that it would take a few days to really sink in.
“We got off to a good start and we really played to our strengths, rowing long and powerful strokes,” he said.
“It's really in the middle of the course that we made the difference and went ahead. And at the end the Danes were finished. They couldn't deliver a sprint finish, as they usually do.”
Tramèr refused to look ahead to Tokyo 2020, saying he would now go back to his medical studies “because life's not only about sport”, he told the paper.
“I'm looking forward to being able to dedicate time to my social life, which I've had to completely put aside for two years. I'm going to be able to go on holiday.”
The gold is Switzerland's second at the Rio Olympics, after cyclist Fabian Cancellara won the men's time trial road race on Wednesday in his final season before retiring.
Heidi Diethelm Gerber picked up Switzerland's first medal at the Rio Games on Tuesday, winning bronze in the 25m pistol shooting event.
A week into the Olympics, Switzerland is well on its way to beating its medal haul in London in 2012, when it picked up two golds and two silvers.