The court, which as unanimous in its ruling, has handed down a sentence of two and half years in prison.
Beltran must also pay compensation of 110,000 kronor ($15,450) to the child he abused and 83,000 kronor to the rape victim.
Citing a risk that Beltran may flee Sweden, the court has also ordered he be remanded in custody, according to statement from the court.
Beltran was charged with raping an 18-year-old nanny in a hotel in southern Sweden during the Rhapsody in Rock concert tour in 1999.
The nanny was caring for the children of Swedish actress Maria Lundqvist during the tour.
The Ystad District Court had earlier given Beltran the minimum sentence of two years in prison for rape.
In the second case, he was charged for having sexually abused an underage girl in Kungsbacka in western Sweden on a number of occasions between 2000 and 2002.
The charges of abuse also brought charged of interference in a judicial matter because Beltran was alleged to have harassed the father of the girl who reported the sex crimes.
He had been acquitted of all charges in the case by the district court in Varberg, but the case was reexamined in conjunction with the appeal of the rape conviction.
In addition to Lundqvist, several other Swedish celebrities have testified in the rape case, including Carola Häggkvist, Robert Wells and Anders Berglund.
The nanny's version of events was primarily supported by testimony from Häggkvist and Lundqvist.
Both cases were taken to the Court of Appeal and combined into a single case at the behest of prosecutor Anna Håkansson, who headed the Ystad rape case.
Prosecutors was asked the appeals court to hand down a sentence of at least three years in prison should Beltran be convicted in both cases, with Håkansson sticking to demands of at least two years for the rape conviction.
Defence lawyers argued that their client should be acquitted of all charges.