10 U.S. Code § 113 - Secretary of Defense
(a) There is a Secretary of Defense, who is the head of the Department of Defense, appointed from civilian life by the President, by and with the advice and consent of the Senate. A person may not be appointed as Secretary of Defense within seven years after relief from active duty as a commissioned officer of a regular component of an armed force.
https://www.law.cornell.edu/uscode/text/10/113
————–
New law not required for Mattis. Congressional waiver, granted by the House Armed Services Committee.
US Congress Passes Waiver for Mattis to Lead Pentagon
Jan 13, 2017
Congress on Friday passed historic legislation allowing retired US Marine Corps Gen. James Mattis to serve as the next defense secretary, overriding some Democrats who took a stand for civilian control of the military.
The move bypasses a law that mandates a seven-year "cooling off" period between military service and assuming the top civilian defense job. Mattis, 66, retired in 2013 after a 44-year military career and serving as commander of US Central Command.
The House voted 268-151, with mainly Republicans — and 36 Democrats — voting in favor. Many Democrats revolted after the Trump transition team backed Mattis out of his commitment to testify before the House Armed Services Committee on Thursday.
https://www.defensenews.com/breaking-news/2017/01/13/us-congress-passes-waiver-for-mattis-to-lead-pentagon/