The 43-year-old is confident both the Barcelona loanee and fellow new arrival Mike van der Hoorn will help the club succeed this season
Barcelona loanee Bojan made his Eredivisie debut on Friday as Ajax eased to a 3-0 win over Roda JC, while Van der Hoorn, a recent acquisition from Utrecht, was an unused substitute.
And De Boer has been pleased with the early efforts of both players, despite their ongoing battles for fitness in pre-season.
"You can see that Bojan is a good player," he told the club's official website.
"Before coming he had not played since April due to a thigh injury. He has fit in very well during the close-season as he was quickly able to play 45 minutes.
"(Van der Hoorn) has had a very tough season. In addition, he was in Israel at the youth European Championship.
"Eventually Mike will fit in well, I expect that he can succeed at Ajax. We now have a full squad which we can work with."
Ajax are aiming for their fourth-consecutive Eredivisie title.