The Spanish champions confirmed the loan on Saturday.
The 22-year-old spent the past two seasons playing in Italy's Serie A, enjoying a reasonable season for AS Roma but barely featuring last term at AC Milan.
A product of Barca's youth academy, Bojan was once regarded as one of the club's the most promising talents but fell out of favour under former coach Pep Guardiola.
He will be coached by former Barca player Frank de Boer at Ajax, who won the Dutch league last season, and will have a chance to compete in the Champions League. – Reuters