The 19-year-old had his medical in Amsterdam on Thursday morning, with the club confirming the move later in the day.
In a statement, the Dutch giants said the attacking midfielder has joined from FC Nordsjaelland in a deal that will last until 2025.
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“Ajax has reached an agreement with Mohammed Kudus and FC Nordsjaelland about the transition from the Ghanaian to Amsterdam,” a statement from Ajax said.
“The multifunctional midfielder / attacker will sign a contract that will take effect immediately and has a term of 5 years, until June 30, 2025.”
Kudus joined Nordsjaelland from the Right to Dream Academy in 2018 and has since developed into one of the most important players at the club.
The teenager has netted 12 times in 26 appearances for the Danish Superliga side this season.