The 17-year-old will join the club next year after agreeing a move to the Santiago Bernabeu.
Real Madrid have agreed a deal to sign Santos wonderkid Rodrygo, according to the Brazilian club.
The transfer, for a reported €45 million fee (£39.3m/$52.2m) is a record a Latin American club, with Santos confirming that they will retain the 17-year-old for another season.
The deal will be completed in July 2019, with Rodrygo set to further his development in Brazil during the 2018-19 campaign.
Santos have praised the conduct of Real throughout negotiations, saying: “Santos FC is grateful for the attitude and professionalism of Real Madrid CF in every process, as well as the family and representatives of the player, who have sought a transparent, and very good, negotiation for all parties.”
Rodrygo has become something of a wonderkid over the past season, scoring six goals and providing two assists in 15 appearances in 2017-18, while he has also scored three goals in four games for Brazil’s Under-17 side. He has been called up to the Under-20 side, but has yet to win a cap.
In addition to the fee Real have paid for the teenager, it has also been reported that €5m (£4.3m/$5.7m) of that figure has been reserved as a bonus for the player.
Rodrygo was the youngest player ever to score a goal in the Copa Libertadores, while he netted six times in one match while playing for the Under-17 side.
He will join another Brazilian prodigy at Santiago Bernabeu when he finally arrives, with the club having agreed a deal to secure Vinicius Junior from Flamengo.
Real have also paid €45m for the 17-year-old, as they look to build an elite team for the future.
He has scored four goals and provided three assists thus far in 2017-18, but his form for the Brazilian Under-17 team is more impressive; he has notched 12 goals in 15 caps.
It was announced that Vinicius would join Real in July, but the teenager revealed earlier this week that he is unsure where he will be playing his football next season.
Santos’ domestic season continues apace, with the club currently 15th in the table, 14 points behind leaders Flamengo.