The 66-year-old singer announced the marriage in a statement to Spanish newspapers.
The wedding took place at the Virgen del Carmen church in the southern jet-set resort of Marbella.
Rev. Roberto Rojo Aguado, one of three priests who celebrated the ceremony, told The Associated Press on Friday that the couple were married Tuesday.
He said the ceremony was attended by two witnesses and the couple's five children. Rijnsburger is 45.
Iglesias was previously married to Isabel Preysler, with whom he had three children.