The court said on Tuesday it had also ruled that Tate and his brother Tristan should be released from police custody immediately. The Tates had been detained for 24 hours pending a ruling on the British arrest warrant.
The court of appeals said in a statement that it "rules to execute the arrest warrant and...to postpone handing over the requested person until the final verdict in the criminal case argued at the Bucharest court".
Tate and his brother Tristan were detained on Monday night on allegations of sexual aggression dating back to 2012-2015, which they "categorically" deny, his PR team said. The warrant was issued by Westminster Magistrates Court in London.
"We are innocent men, we are very innocent men and in time everyone is going to see that and we are very excited to finish this judicial process and clear our names," Tate said as he was released from police custody.
"It's very funny because I've been asking Romanian courts to go to the UK myself. I've asked five times and been declined so now I get to go home. That's fantastic news," he said.
British police told Reuters the Tates were part of an ongoing investigation into allegations of rape and human trafficking, adding they were working with Romanian authorities.
"We appreciate the Bucharest Court of Appeal's decision to postpone the extradition of Andrew and Tristan Tate," Eugen Vidineac, legal counsel for the defendants, said in a statement.
"This ruling provides an opportunity for the brothers to participate fully in their defence and for the legal process to proceed in a transparent manner."
Tate, who gained millions of fans by promoting an ultra-masculine lifestyle, was indicted in June in Romania along with his brother and two Romanian women for human trafficking, rape and forming a criminal gang to sexually exploit women. They have denied the charges.
The case has since been with the Bucharest court's preliminary chamber, which needs to decide whether the trial can start. A decision has yet to be made, with Romanian courts backlogged.
The Tate brothers were held in police custody pending the criminal investigation from late December 2022 until April, to prevent them from fleeing the country or tampering with evidence. They were placed under house arrest until August.
They have since been under judicial control, a lighter preventative measure meaning they have regular check-ins with the police but can move around freely except for leaving the country.
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