Huijsen will join the Spanish side now the Premier League season has concluded, after it was confirmed that the side had agreed to meet his £50million release clause.
He could make his debut as soon as next month in the Club World Cup.
Asked after his final game for the Cherries about his performances and moving to Madrid, Iraola said: “Dean has been very good, probably for someone of his age, he has been above our expectations that obviously were high because that's the reason we signed him.
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“But his performance has come probably earlier than we expected and obviously it's a big change for him.
“He's going to Real Madrid, but I think he's ready.
“Obviously he will have to continue his progression, but also he goes to play with a manager that I know very well [Xabi Alonso – Iraola and Alonso played youth football together] and will be the best teacher now for him.”
Huijsen bid farewell to the Bournemouth fans with a speech on the Dean Court pitch, ending in a rendition of his chant – ‘Deano again, ole, ole’.
Asked about what was a nice moment between the 20-year-old and the Cherries faithful, Iraola said: “I've liked also how the supporters, the fans have reacted, I think have rewarded him and it's a way of saying you've been very good, thank you.
“I think it's also something from Dean that he wanted to play the last two games, to do well, to finish well and I think it has been a nice moment.
“For me today also to get some time to meet the family of my players, of the staff, their kids, their parents.
“It’s always lovely because they are very important for them and I think it's a nice moment.”