The office of the governor of the Territory of Wyoming was established by Congress on July 25, 1868, with the passage of the Organic Act creating the Territory of Wyoming. Section 2 of the act provided that the office of governor would be filled by presidential appointment, with confirmation by the United States Senate. Gubernatorial powers and duties set forth in the act included command of the territorial militia, superintendency of American Indian affairs, legislative veto power, the power to pardon offenses against territorial laws, and the authority to fill appointive offices.

Following the appointment and confirmation of John A. Campbell as the first governor of Wyoming Territory, and the organization of territorial government, the responsibilities of the governor's office increased as the government developed. During its first session in 1869, the territorial legislative assembly empowered the governor to reprieve a person under the sentence of death (Chapter 74, General Laws of the Territory of Wyoming, 1869). Two years later, with the passage of an act entitled Volunteer Militia, pages 116-117, Session Laws of the Territory of Wyoming, 1871, the governor was required law commission officers elected by the members of volunteer militia companies. The act also empowered the governor to furnish arms and equipment to the militia companies, and authorized him to call them into action. Other territorial legislation required the governor to make offers of reward for fugitive felons if requested by the prosecuting attorney of the county in which the crime had been committed.

Starting in 1888, statue required that territorial officers and boards of public institutions submit reports to the governor. Fiscal officers were charged to report annually, while other officers reported biennially. Today, elected officials and agencies of the executive branch of state government are required to submit annual reports to the Department of Administration and Fiscal Control, Research and Statistics Division, for use by the governor and the state legislature (9-2-1024, Wyoming Statutes Annotated, 1977).

The Wyoming State Constitution, drafted and ratified in 1889, established various powers and duties of the governor, in addition to those prescribed by the Organic Act and enactments of the territorial legislative assembly. Article 4, Sections 4 and 9, and Article 5, Section 4, Constitution of the State of Wyoming, empowered and directed the governor to convene extraordinary sessions of the state legislature, to deliver a message to each state legislature concerning the condition of the state, to veto items in appropriation bills, to appoint supreme court and district court judges, to transact all necessary business with the officers of the state, to expedite all matters resolved by the legislature, and to faithfully execute all laws of the state.

Qualifications set forth in the state constitution to hold the office of governor, included being a citizen of the United States, a qualified elector of Wyoming, at least thirty years of age, and a resident of the state, or territory, for five years preceding his election. The governor is not eligible, under the constitution, to hold any other office during the term for which he is elected.

The governor is also authorized to serve on state government boards and commissions, participate in interstate stream negotiations and contracts, preparing civil defense plans (originally through the Civil Defense Agency, later called the Emergency Management Agency), administrative control over Executive branch state agencies, designating state agencies to administer federally supported cooperative programs, and appointing Wyoming residents to any committees required by the programs.