The 26-year old French striker has penned a three-year deal with the Romanian club on a free transfer after rejecting an offer of an extension from the Saints.
"This is a fantastic move for Gregory,” said his agent Ricky Gillies.
"He came to Scotland from France in 2006 and joined Forfar when they were in the Third Division. He worked his way to the SPL the hard way. Now he's got his move to a big club in Europe and it is thoroughly deserved.
"It's a fantastic story for a young guy from Nantes and shows what hard work can do.
"Cluj have been in the Champions League a couple of times in recent years and played Chelsea on one of those occasions. They have got big ambitions to get back there and that is something that has excited Gregory.
"And the move to Romania opens up a whole new market for him too. Russia and Ukraine are close by and have some really big clubs now.
"There's a chance he could catch their eye and earn himself another big switch."