AI in Government Act of 2019 This bill creates the AI Center of Excellence within the General Services Administration to promote the efforts of the federal government in developing innovative uses of and acquiring artificial intelligence (AI) technologies, improve cohesion and competency in the adoption and use of AI within the federal government, and undertake such activities for the purposes of benefitting the public and enhancing the productivity and efficiency of federal government operations. The Office of Management and Budget (OMB) must (1) issue a memorandum to federal agencies regarding AI governance approaches, to be followed by preparation and submission of governance plans by the agencies and updates at specified intervals; and (2) issue a draft version of the memorandum for public comment and submit to Congress a comprehensive plan with a time line to complete requirements of this bill. The bill requires agencies that use or anticipate using AI to submit to the OMB and post on a publicly available page of the agency website a plan to achieve consistency with the memorandum. In addition, the Office of Personnel Management must, among other things identify key skills and competencies needed for positions related to AI; and establish an occupational series, or revise an existing job series, to include positions the primary duties of which relate to AI.