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.