Perez, who took up his job in December 2004, is leaving Nike because of differences with Philip Knight, Nike founder and chairman.
Knight said: "Succession at any company is challenging, and unfortunately the expectations that Bill and I and others had when he joined the company a year ago didn't play out as we had hoped. I want to personally thank Bill for his dedication and commitment over the past year."
Parker has shared the role of president of the Nike brand with Charlie Denson since 2001. He has been with the company since 1979 and has held roles in product design, development, marketing and brand management. He is also credited by Nike as being the executive behind the lucrative Nike Air franchise.
Denson, who started as an assistant in a Nike store in 1979, will remain the sole president of the Nike brand.
Parker said: "I am committed to continue delivering profitable growth for our shareholders, creating distinctive product innovation and compelling brand connections for consumers, and building strong relationships with our retail partners."
Nike retains Wieden & Kennedy, Portland, as its advertising agency of record.
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