The former Newcastle defender agreed terms and passed a medical at Pride Park prior to putting pen to paper and becoming Rams' manager Billy Davies' sixth signing of the summer.
"Andy is an excellent player, calm head and has a very good attitude," Davies told Derby's official website.
"Like Andy Todd he brings experience to the squad.
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"I believe Andy has great years ahead of him. Every time I see him play he shows how consistent he is.
"We're very pleased to have him on board."
Stoke were also in the hunt for Griffin after the 28-year-old enjoyed a successful loan period at the Britannia Stadium last season, but ultimately the lure of top flight football proved too strong for the versatile defender's signature.
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