The brothers are also charged with forming a criminal gang to sexually exploit women.
It is not clear under what conditions the Tates - who are keen supporters of US President Donald Trump and boast millions of online followers - were allowed to fly out of Romania.
An official at the Ministry of Internal Affairs, who spoke on condition of anonymity because they were not authorised to discuss the case, said the decision was at the discretion of prosecutors.
Romania's anti-organised crime agency, DIICOT, said on Thursday that prosecutors approved a "request to modify the obligation preventing the defendants from leaving Romania", but that judicial control measures remained in place.
The agency did not say who had made the request.
"These include the requirement to appear before judicial authorities whenever summoned," the agency said.
"The defendants have been warned that deliberately violating these obligations may result in judicial control being replaced with a stricter deprivation of liberty measure."
Andrew Tate, 38, and Tristan Tate, 36 - who are dual US-British citizens - were arrested near Romania's capital in late 2022 along with two Romanian women.
Romanian prosecutors formally indicted all four in 2024.
In April, the Bucharest Tribunal ruled that a trial could start but did not set a date.
All four deny all of the allegations.
Andrew Tate is known for expressing misogynistic views online and has repeatedly said that prosecutors have no evidence against him and that there is a political conspiracy to silence him.
He was previously banned from various social media platforms for misogynistic views and hate speech.
The Tates' departure came after Romania's Foreign Minister Emil Hurezeanu said earlier in February that a US official under the current Trump administration had expressed interest in the brothers' legal case in Romania at the Munich Security Conference.
The minister insisted it did not amount to pressure.
In December a court in Bucharest ruled that the case against the Tates and the two Romanian women could not go to trial because of multiple legal and procedural irregularities on the part of the prosecutors.
That decision by the Bucharest Court of Appeal was a huge setback for DIICOT, but it did not mean the defendants could walk free.
The case has not been closed, and there is also a separate legal case against the brothers in Romania.
with Reuters
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