The Dutch champions have beaten off competition from the likes of Chelsea and Manchester United to sign the highly-rated 18-year-old striker
The capture of the highly-rated 18-year-old striker on a four-year deal looks to be a significant coup for the club, who have reportedly beaten a host of potential suitors in the race for his signature.
The likes of Manchester United and Chelsea were said to be keen on securing his services after he became a free agent following his departure from Dinamo Zagreb.
A club statement read: "Ajax have reached [an] agreement with Robert Muric.
"He signs a contract which begins on July 1, 2014, and runs until June 30, 2018.
"The 18-year-old youth international played last season with Dinamo Zagreb. There will be a number of formalities to be fulfilled before Muric [will] play for Ajax."
Muric scored twice for Croatia at last year's FIFA Under-17 World Cup.