Ben Ali -- who now lives in exile in Saudi Arabia -- only used the plane once to test it before it was outfitted.
The Turkish firm bought the Airbus A340 for 181 million dinars ($78 million), Tunisair spokeswoman Amal Bourguiba said, without giving a date for the sale.
The A340 had arrived in the French airport of Bordeaux in the autumn of 2010 to be equipped for Ben Ali's use, but a popular uprising in Tunisia toppled the dictator early the next year.
Tunisair, in a statement later on Sunday, said it had obtained a good price, compared with the 250 million dinars paid in 2009 to order the plane, and said it would save on the parking costs in Bordeaux.
According to French daily Sud-Ouest, Ben Ali -- who now lives in exile in Saudi Arabia -- only used the plane once to test it before it was outfitted.
Tunisair put the plane on the market in January 2012, saying it had been outfitted with a living room and bedroom "to suit the travel needs of a head of state".
Another Airbus A340 -- this one luxuriously furnished for slain Libyan president Moamer Kadhafi -- has also been grounded for years at the French airport of Perpignan.
The plane, which a Kuwaiti firm was once interested in buying, still in theory belongs to Libya, a country that has been wracked by chaos since the 2011 revolt that toppled and killed Kadhafi.