Veterans' Outreach Act of 2013 - Directs the Secretary of Veterans Affairs (VA) to carry out a two-year demonstration project to assess the feasibility and advisability of using state and local government agencies and nonprofit organizations to increase veteran awareness of available benefits and services, and to improve the coordination of outreach activities between the Secretary and federal, state, and local government and nonprofit providers of health care and benefit services for veterans. Allows the Secretary to extend such program for an additional two years.

Authorizes the Secretary to enter into cooperative agreements with various state departments and agencies concerning the provision of veterans' activities.

Requires the Secretary to include, in annual VA budget justification materials, a separate statement of amounts requested for outreach activities of the VA in aggregate as well as for each of the Office of the Secretary, the Veterans Health Administration, the Veterans Benefits Administration, and the National Cemetery Administration.

Directs the Secretary to establish: (1) an advisory committee on VA outreach activities; and (2) for each VA medical center, an advisory board relating to outreach activities at such center.

Changes from biennial to annual a required report to Congress on VA outreach activities. Requires the inclusion in each report of recommendations: (1) to maximize resources for VA outreach activities, and (2) to focus such efforts on activities proven to be more effective.