The 28-year-old Cameroon international officially signed on a free transfer from Chelsea on Friday when he was granted a work permit, but it is alleged he picked up a £2m signing on fee.
Geremi agreed a three-year contract.
Allardyce: "We have signed a player who is a real winner and who has played on the biggest stages for both his clubs and his country.
"He's been at Real Madrid and he's been at Chelsea, two of the top clubs in Europe, and that tells you he must be a quality player.
"It's a great bit of business for us and he's very keen to be successful at Newcastle United, as we all are, in the times ahead.
"I still think that when you are targeting players like Mark Viduka, Joey Barton and David Rozehnal you have to stave off a lot more competition than we did with the sort of players I was bringing in at Bolton.
"That makes it hugely difficult. You have got to do a lot of selling of yourself and the football club in terms of what you are trying to achieve.
"I think we have done that extremely well, given the sort of competition we were up against for all three players."
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