Michael Voudouri fled to Northern Cyprus in October 2012 after pleading guility to a £10.3 million tax fraud.
Mr Voudouri, of Bridge of Allan, Stirlingshire, was arrested at his Cypriot home in January after allegedly using a fake passport.
Last night, his Glasgow-based lawyer Aamer Anwar said his client would voluntarily consent to the extradition after reaching an agreement to have the passport charges dropped.
Mr Anwar said: "I had already approached the Lord Advocate's team to advise a few weeks ago that Mr Voudouri wished to return voluntarily to the UK and for arrangements to be made to expedite the process. As a result Mr Voudouri consented to the extradition and Scottish officers will within the next 10 days bring him back to Scotland."
A Crown Office spokesman said: "We are aware that Michael Voudouri is currently in custody in the Republic of Cyprus and we will continue to liaise with the Cypriot authorities regarding his extradition to Scotland."