That's according to publishers Namco Bandai Partners, who are only aware of a few "dribs and drabs".
"I can't give you a number, but what I mean by an 'amazing success' is that all the stock we built of the Black Phantom Edition has sold out (apart from dribs and drabs)," Lee Kirton, marketing and PR manager for Namco Bandai Partners UK, told Eurogamer.
"For a game that's been out a long time overseas we believe it to be a success. Reviews scores and coverage have been amazing.
"We haven't done hundreds of thousands of units," he added, "but we've been pleased."
The Black Phantom edition included an art-book, strategy guide and soundtrack. Namco Bandai Partners will release a standard edition of the game this week.
The success of Demon's Souls never ceases to amaze us. We suspect Sony will want to make a much bigger deal out of the inevitable sequel, should it roll around any time soon.