Governors are appointed by the President of the United States and confirmed by the Senate for staggered 14-year terms.

http://en.wikipedia.org/wiki/Federal_Reserve_System

Governors are appointed by the President of the United States and confirmed by the Senate for staggered 14-year terms.One term begins every two years, on February 1 of even-numbered years, and members serving a full term cannot be renominated for a second term.