Both clubs confirmed the transfer on Wednesday, with terms initially described as undisclosed.
Portuguese outlet Record has since added further detail, reporting that Benfica will receive €3.5m (£3m) for the 21-year-old.
Benfica have also retained a 20% sell-on clause, meaning they stand to benefit further if Brighton sell the player on in future.
The length of the contract, running through to 2031, underlines the scale of Brighton's ambition for the young winger.
Rêgo made five first-team appearances for Benfica last season, including his debut in the Champions League.
He came off the bench late in Benfica's 2-0 win over Ajax in November, before making his first league start four days later in a 2-1 victory over Nacional.
Those outings marked his first real taste of senior men's football after progressing through the youth ranks.
Technical director Mike Cave said the club were pleased to secure a player they regard as an exciting talent for the future.
"Rodrigo is an exciting talent who we're really pleased to bring to the club," Cave said.
"He got his first taste of men's football last season in both the league and Champions League, which is a reflection of the progress he's made.
"We believe we can help him continue his development and reach his full potential. We're looking forward to working with him on this next step."
Rêgo's route to Benfica came via the academies of Porto and Famalicão, where he first developed as a winger before making the move in 2023.
Brighton have built a reputation for identifying and developing young talent from across Europe, and the length of Rêgo's contract suggests the club see him as a long-term project rather than an immediate first-team option.
His progress will now be closely monitored as he adapts to a new league, a new country and a new stage in his development.
The sell-on clause retained by Benfica is a common feature of deals involving highly rated young players, giving the Portuguese club a continued financial interest in Rêgo's career even after his departure.
For Brighton, the addition of another promising young talent fits a familiar pattern, with the club having built much of its recent transfer strategy around developing young players with resale value of their own.
Rêgo will now begin pre-season with his new teammates as he looks to build on the limited senior minutes he collected during his final campaign in Portugal.