The Ankara administrative court was set to inform telecommunications regulator TIB of the decision, and access to Twitter was expected to be restored later in the day, private NTV television said.
The government signalled it would abide by the judicial ruling, with Deputy Prime Minister Bulent Arinc telling reporters in the capital that "if the court gave such a decision, we will implement it".
The Twitter ban took effect on March 20 after Erdogan defiantly vowed to "wipe out" the online messaging service, saying it had failed to abide by hundreds of court orders to remove content deemed illegal.
The UN high commissioner for human rights was among international figures and national leaders who condemned the ban on the US-based site as curbing free speech.
Erdogan's political opponents welcomed the court order.
"It was impossible for a totalitarian regime to silence the technology," said Emrehan Halici, deputy head of the main opposition Republican People's Party.
"It was a shame to try to shut down Twitter. It has done nothing other than humiliate our country," he told AFP following the court's decision. "More people than before have taken to Twitter after the ban."
Among those defying the ban were several cabinet members as well as President Abdullah Gul, who set himself publicly at odds with Erdogan by denouncing the move as "unacceptable".
The ban came as social media networks have been flooded almost daily with leaked phone recordings in which Erdogan can allegedly be heard interfering in court cases, trade deals and media coverage.
The firebrand premier has denounced most of them as fakes and part of a "vile attack" by rivals, including a former ally, the US-based Muslim cleric Fethullah Gulen, many of whose followers have held positions in the police force and judiciary.
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