The teenager has made over 40 first-team appearances in the Danish top flight and rejected interest from two English sides to sign for the Eredivisie champions
Sporting director Marc Overmars announced on Thursday night that the club would sign a young forward on the final day of the transfer window.
The Amsterdam giants then announced the acquisition of the teenager, who has already made more than 40 league appearances in the Danish league, on their official website.
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The youngster’s performances in his homeland had previously attracted attention from Premier League side Liverpool and Overmars sees a bright future for the versatile attacker.
“The fact that Lucas has played so many matches in the Danish League at such a young age indicates that he is a great talent,” the former Ajax and Arsenal legend told Ajax.nl.
“He will join the first team after the internationals. I expect him to further develop in the senior side. He's a very interesting player for us because he's a versatile attacker who can even play in the No.10 position.
“So we are delighted that he has chosen to sign for Ajax because there was a lot of interest in him, including two English clubs. We are fortunate that Ajax has a good name in Scandinavia as many talented players are given a chance here.”