Reducing Environmental Barriers to Unified Infrastructure and Land Development Act of 2019 Act or the REBUILD Act This bill authorizes (1) the assignment to states of federal environmental review responsibilities under relevant federal environmental laws for projects funded by, carried out by, or subject to approval by federal agencies; and (2) states to assume all or part of those responsibilities. Each responsible federal official who is authorized to assign such responsibility must promulgate regulations that establish requirements relating to information required to be contained in state applications to assume those responsibilities. An official may approve an application only if (1) public notice requirements have been met, (2) the state has the capability to assume the responsibilities, and (3) the head of the state agency having primary jurisdiction over the projects enters into a written agreement with an official to assume the responsibilities and to maintain the financial resources necessary to carry them out. The officials must audit state compliance with federal laws for which responsibilities are assumed. The officials may terminate the responsibilities assigned to states after providing notice to states of any noncompliance and an opportunity to take corrective action.