Strategic Withdrawal of Agencies for Meaningful Placement Act of 2022 or the SWAMP Act This bill prohibits new construction, major renovation, leasing, or renewing a lease of certain executive agency headquarters in the District of Columbia metropolitan area and establishes a competitive bidding process for the relocation of such headquarters. The General Services Administration (GSA) must (1) establish a process to allow an executive agency to request the GSA to issue a solicitation for the relocation of its headquarters or allow the GSA to issue such a solicitation without a request, if necessary; (2) allow any state to respond to a solicitation with 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.