The 21-year-old, who scored 13 goals during a loan spell at Dutch second division outfit Fortuna last season, describes the move to the Amsterdam ArenA as a childhood dream.
"Unbelievable," he told Algemeen Dagblad. "The biggest club in the Netherlands. As a young boy you dream of that.
"Initially, I could hardly believe Ajax was interested, but after I spoke with Marc Overmars I knew it was serious.
"For what position have I been signed? I have been told that I have been bought for the striker position. First I have to acclimatise to the level, but with better players around me I hope to adapt quickly."
The Cottagers are expected to receive a fee in the region of £395,000 for Hoesen, who has agreed a three-year deal with the Eredivisie giants.