Kellogg purchased Pringles after a similar deal between P&G and Diamond Foods fell through because of accounting issues and executive changes at Diamond Foods.
Kellogg's acquisition of Pringles will help it in its plans to become a global player in snacks, as it is in cereal foods.
P&G and Diamonds Foods, which makes Emerald Nuts, said they had mutually agreed to end their deal regarding Pringles.
Pringles reported $1.5bn (£956m) in annual sales in its latest figures, across 140 countries.
It is unclear at this stage whether the deal will lead to any redundancies.
John Bryant, Kellogg president and chief executive, said he was confident that the Pringles business "would thrive under Kellogg's leadership."
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