Said Mansour is the first person to be stripped of his Danish citizenship under a law introduced in 2004.
The Supreme Court today rejected his appeal of a lower court decision to revoke his citizenship and expel him after a four-year prison sentence.
Mansour, who is 56 and has lived in Denmark for 32 years, was convicted of instigating and promoting terrorism by posting social media messages in support of al-Qaida and associated groups. Mansour denied the charges, citing the freedom of speech.