The Governing Body of Green River consists of a Mayor and six elected Council Members. There are three wards within the City limits
, with two Council Members representing each ward. Council Members must live within their designated ward and must be properly registered as a Sweetwater County voter. A person must file an application with the City to run for a City Council position. Filing applications may be obtained from the City Clerk at City Hall. As set by State Statutes, filing must be accomplished within the prescribed deadline.
Citizens elect Council Members to staggered four-year terms. There is no limit to the number of terms a Council Member may serve. Council Members may serve on standing committees appointed by the Mayor.
The Council's major functions and duties are primarily legislative. Council directs City affairs by passing ordinances or adopting resolutions. Either may be introduced by a Council Member at a business meeting, but ideas for them also may originate from citizens or the City staff.
The Mayor of Green River is the chief elected official of the City, with all the powers and duties of a Council Member. The Mayor also appoints most Council committees, their chairmen, and many members of City advisory boards and commissions, with Council approval. He signs all ordinances and bonds authorized by the Council. The Council elects one of its members a Council president to serve temporarily in the Mayor's absence or disability.