Tarik Chadlioui, accused of being a recruiter for the Islamic State (ISIS) through extremist videos, had claimed he is an "anti-terrorist preacher" in his bid to fight extradition at Westminster Magistrates' Court in London last week.
His lawyers were fighting against his extradition on the grounds that it will be "a clear interference with his right to a family life".
But Chief Magistrate Emma Arbuthnot rejected the claim, saying Chadlioui's family were eligible for state-funded social care benefits and could seek help from his mosque.
Chadlioui was one of six people arrested across Europe in June this year as part of a Spanish investigation into support for the terrorist group.
Spanish authorities allege that Chadlioui made three videos for extremist forces in Syria during two visits to Mallorca in 2014 and 2015. The 43-year-old faces a charge of collaboration with, or membership of, an armed group for which the maximum sentence is 20 years' imprisonment.
"He has uploaded thousands of videos to YouTube. This is what he does, he is an anti-terrorist preacher," Malcolm Hawkes, Chadlioui's barrister, had told Westminster Magistrates' Court last week.
Spanish authorities believe he is behind radicalising one of the terrorists Omar Mostefai who killed 89 music fans at the Bataclan theatre in Paris in November 2015 before blowing himself up.
He has also been linked with Anjem Choudary, a radical Muslim cleric currently in a UK jail for supporting the ISIS.
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