After initially missing out on the winger on deadline day in January, they have now signed him.
Should the teenager join another English side at the end of his current deal, continental clubs would only need to pay a nominal fee, while Cottagers are entitled to compensation.
On July 1st, the 19-year-old will join the club.
Ahead of a transfer which will see a fee of 5m plus add-ons, Carvalho underwent a medical.
The deal for Carvalho fell through after the Premier League side ran out of time.
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The Championship leaders were set to sign Carvalho and loan him back to the Cottagers for the rest of the season, but he remained with them anyway.
In the FA Cup loss to Manchester City, Carvalho scored his 11th goal of the season.
The club was ordered to pay a record compensation fee for a 16-year-old in 2021. If add-on clauses are met, Cottagers could receive a fee in the region of 4 million dollars and have a substantial sell-on clause.
Sky Sports' Nick Wright.
The clamour of January's Deadline Day when the Reds failed to sign the player from the Cottagers was nothing new. The biggest clubs in the country have been vying for his signature for years.
Balham FC, the first club in England to be founded by Greg Cruttwell, was caused by the interest in the 3G pitches and concrete courts of south by Carvalho.
Representatives from Manchester United went to meet him. He was taken on a tour of the headquarters. There were meetings with every club under the sun.
He and his family, who had moved to London from Lisbon only a few years earlier, turned down more prestigious offers in favor of a move to Fulham. The decision has paid off.
The feature can be read in full here.
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