The action followed the Swiss Supreme Court's rejection of an appeal from Muhammad Achraf, whose Spanish-based group is suspected of plotting to bomb the National Court in Madrid, said Justice Ministry spokesman Folco Galli.
Under the escort of three Spanish police officers, Achraf flew on Friday afternoon from Zurich to Madrid, Galli said.
He said Achraf had been in detention in Switzerland since 21 October.
"Spanish authorities suspect him of being a directing member of a radical Islamic cell and to have prepared with other people an explosive attack against a court in Madrid," he said.
He noted that the Swiss high court, the Federal Tribunal, had rejected Achraf's contention that he would be in physical danger should he be extradited to Spain.
"Spanish authorities suspect him of being a directing member of a radical Islamic cell and to have prepared with other people an explosive attack against a court in Madrid"
Swiss justice ministry spokesman
Spanish authorities suspect Achraf of masterminding a plot to ram a truck loaded with 500kg of explosives into the court, which is a hub of anti-terror investigations.
Achraf is thought to be Algerian but travelled using several fake identities.
He was arrested in Switzerland for an unrelated offence.
He was in custody pending trial in Bern in connection with attack preparations that might have taken place in Switzerland, officials said.
However, Swiss authorities decided that priority had to be given to Spanish criminal proceedings.