The court also said that last month’s ban must be lifted, sending a statement to Turkey’s media regulator and the government.
It remains unclear whether the verdict will lead to a lifting of the block.
PM Recep Tayyip Erdogan had vowed to “wipe out Twitter” after users spread allegations of corruption.
Twitter itself has filed a challenge to the access ban.
On Wednesday, the constitutional court in Ankara sent its ruling to Turkey’s telecommunication authority (TIB) and the transport and communications ministry.
The court asked them to “do what’s necessary” to lift the ban, Turkey’s NTV television reported.
The authorities have so far made no public comment on the verdict.
A ban was imposed on March 21 on the grounds that Twitter had failed to remove the allegations of corruption involving senior officials.
A number of complaints were filed to courts, arguing the ban was illegal and unconstitutional.
The administrative court in Ankara later issued a temporary injunction ordering the TIB to restore access to Twitter until it could deliver its full verdict on the ban.
Meanwhile, users across Turkey have found many ways of circumventing the prohibition, which has been widely criticized and ridiculed.
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