Ajax have reached the semi-finals in spectacular style after beating Juventus 3-2 on aggregate - following a 2-1 win in the second leg in Turin - defying all expectations to make the last four of the tournament.
They have not had an easy run, either. The Eredivisie outfit met Bayern Munich in the group stages, reigning champions Real Madrid in the last 16 and Cristiano Ronaldo's Juventus in the quarter-finals.
However, just one loss across six games against those European giants has put Ajax within touching distance of the final, and old boy Van der Vaart is confident they will make it now, along with Barcelona, who defeated Manchester United 4-0 on aggregate to ease into the final four.
"Ajax were much better than Juventus in the second half [in Turin]," Van der Vaart told the BBC.
"We talk about going to the gym and being strong and quick, but they can all play with the ball and, in the end, clever football wins.
"I never thought they could get this far but it is so nice to see everyone scared to play against Ajax. Johan Cruyff is our pride and the best player we've ever had, and I'm so happy two of his teams are in the semi-finals. I'm 100% sure they are going to play each other in the final."
Van der Vaart also reserved special praise for Barcelona-bound midfielder Frenkie de Jong, an integral part of the attractive, intricate, high-pressing football Ajax are playing.
"Frenkie de Jong was one of my favourites tonight even though he didn't play his best game. They play like a team and when you play away in Italy and your goalkeeper doesn't make a save, it is fantastic."
Ajax's next opponents will be either Manchester City or Tottenham, with the latter holding a slender 1-0 advantage from the first leg in London. Meanwhile, Liverpool are widely expected to be Barcelona's next opponents after the Reds beat Porto 2-0 at Anfield in their first meeting.