Portugal lost to Chile in penalty kicks in the semi-final on Wednesday in Kazan.
"The president of the Portuguese Football Federation and the national team coach understand that, given that it is impossible to achieve the objective of winning the Confederations Cup, we should release the player so that he can, finally, get to know his children," the federation said in a statement on Thursday.
The federation also praised Ronaldo, who had informed it of his children's birth before ahead of the tournament, for representing the national team at the tournament "in a gesture that we should emphasise and extol".
The Portuguese squad will play for third place on Sunday against the loser of the second semi-final between Mexico and Germany on Thursday night in Sochi.
After Portugal's loss to Chile, Ronaldo wrote on his Facebook page he was "very happy to be finally be able to be with my children for the first time".
Portuguese media have reported that the twins were born to a surrogate mother. Ronaldo is also the father of a boy named Cristiano Ronaldo Jr, who was born in 2010. He has not revealed the mother's identity.
The Real Madrid star is currently embroiled in a tax fraud case in Spain.
The Spanish prosecutor says Ronaldo knowingly used a business structure to hide his image rights income in the country between 2011 and 2014. Ronaldo has denied the charges.
(Reporting by Moscow newsroom; Editing by Angus MacSwan)
