A bill to amend the Internal Revenue Code of 1986 to extend the work opportunity credit to certain recently discharged veterans, to improve the coordination of veteran job training services between the Department of Labor, the Department of Veterans Affairs, and the Department of Defense, to require transparency for Executive departments in meeting the Government-wide goals for contracting with small business concerns owned and controlled by service-disabled veterans, and for other purposes.

Veteran Employment Transition Act of 2013 - Amends the Internal Revenue Code to revise the definition of "qualified veteran" for purposes of the work opportunity tax credit to include recently discharged veterans.

Requires the Department of Defense (DOD) and the National Guard to inform military personnel who are discharged or released from active duty of the work opportunity tax credit and provide them with documentation relating to eligibility for and use of such credit.

Veterans Employment and Training Services Act of 2013 or the VETS Act - Requires the Secretaries of Labor, Veterans Affairs, and Defense to enter into an agreement to govern the coordination of veteran job training services. Requires the Secretaries of Labor and Veterans Affairs to prepare reports on the veteran job training programs of their respective departments.

Amends the DOD pilot program for assessing the feasibility and advisability of permitting enlisted personnel to obtain civilian credentialing or licensing for skills required for military occupational specialties to require the designation as military occupational specialties of the MOS 31B Military Police, MOS 15Q AC-Air Traffic Controller, and the MOS 12M Fire Protection, in addition to not fewer than three and not more than five additional military occupational specialties.

Honoring Promises to Service-Disabled Veterans Act of 2013 - Amends the Small Business Act to direct the head of each executive department to submit an annual report to the Administrator of the Small Business Administration (SBA) containing the percentage of the total value of all prime contracts awarded by the executive department during the preceding one-year period to small business concerns owned and controlled by service-disabled veterans.