The 16-year-old has been likened to fellow Frenchman and Red Devils ace Paul Pogba for his box-to-box style running and sheer strength.
He has already captained the national side at U17 level and was said to have attracted the likes Manchester City and Juventus prior to signing for United’s youth set-up.
Footage taken while playing for France shows Traore running from his own half into the opposition box, before calmly slotting into the back of the net.
The industrious midfielder is unlikely to see first-team action for a while, but that hasn’t stopped fans buzzing to see him in action.
“I’m so glad Mourinho is investing in youth,” one wrote. “It's the Manchester United way.”
Another added: “He is going to learn so much from Pogba.”
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Following the announcement, U18s coach Kieran McKenna told MUTV the club had been looking at the youngster “for a while”.
“He is a really powerful midfielder who likes to run box to box,” he said.
“He is very strong technically and is improving all the time.
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“He's a nice man and his English is improving. He's settling in well with the boys and has taken to the club really well.”
Traore made his debut in United’s 3-2 defeat to Wolves on Saturday, in the U18 Premier League Cup.
He turns 17 in January and should be eligible for the FA Youth Cup campaign.