Strategic Withdrawal of Agencies for Meaningful Placement Act of 2019 or the SWAMP Act This bill repeals the requirement that all offices attached to the seat of government be exercised in the District of Columbia, and not elsewhere. It prohibits new construction or major renovation of certain executive agency headquarters in the Washington Metropolitan area. The General Services Administration (GSA) must (1) establish a process to allow an executive agency to request GSA to issue a solicitation for the relocation of its headquarters; (2) allow any state to submit a proposal for the relocation of the agency's headquarters; and (3) in consultation with the executive agency, select a state for the relocation of the agency's headquarters using a competitive bidding procedure based on certain considerations.