Woods won the Republican nomination for the Senate seat in a hotly contested primary race and is unopposed in the general election.
Harden, a Clovis Republican, has served in the Senate since 2002. He was in the cabinet of then-Gov. Gary Johnson as the secretary of an agency now called the Department of Workforce Solutions.
In a letter of resignation to the secretary of state's office dated Thursday, Harden said he was stepping down effective Friday.
GOP Gov. Susana Martinez will appoint Harden's successor from names submitted by the boards of county commissioners of each county in the eastern New Mexico Senate district.