Simon Corner, 33, was detained in Copenhagen on a European Arrest Warrant on April 14th and on Tuesday a court approved his extradition to Spain where he is wanted for questioning over his girlfriend's disappearance.
The 32-year-old, who moved to Spain from Alexandria in West Dunbartonshirewhen she was 18, vanished without trace from her home in Guadiaro, southern Spain on November 4th.
She worked in Gibraltar and has a nine-year-old son from a previous relationship who is being looked after by his father since she disappeared.
Corner was initially questioned by Civil Guards over his girlfriend's disappearance but then skipped the country when a second interview was requested.
An investigating magistrate at San Roque court issued an arrest warrant but he has yet to be charged with a crime.
A Foreign Office spokesman confirmed: "We are providing assistance to a British man arrested in Denmark."
Helen Jordan, Brown's sister who set up a facebook page appealing for information regarding her missing sister said the family was "delighted" that Corner had been caught.
"While we are delighted that he's been caught,we still have a long road to go," she wrote on the Find Lisa page.
"This page that was set up to 'Find Lisa' turned into 'hunt Simon' so our journey is not over, and we still appeal to anyone that knows where she might be to contact the guardia."