Ending Homelessness Act of 2017 This bill amends the McKinney-Vento Homeless Assistance Act to make additional FY2018-FY2022 appropriations available for: (1) emergency relief grants to address the unmet needs of homeless populations in jurisdictions with the highest need, (2) rental assistance under the United States Housing Act of 1937 for persons and households who are homeless, and (3) homeless outreach and coordination services. Beginning in FY2018, the bill provides annual additional funds for: (1) the Housing Trust Fund to provide grants to states for use to increase homeownership and the supply of rental housing for extremely low- and very low-income families, including homeless families; and (2) incremental project-based voucher or rental assistance under the Federal Housing Enterprises Financial Safety and Soundness Act of 1992. During the first five fiscal years such amounts are made available, the Department of Housing and Urban Development (HUD) must ensure that priority for occupancy in dwelling units located in housing that was provided or is receiving such assistance be given to persons and households who are homeless. When HUD allocates grants to states from the fund for rental housing, the dwelling units must be subject to legally binding commitments to ensure that the residing family's contribution toward rent does not exceed 30% of the family's adjusted income. The bill provides funding to HUD to expand the Healthcare and Housing (H2) Systems Integration Initiative by assisting states and localities in coordinating policies among Medicaid programs, behavioral health providers, housing providers, and finance support services for homeless persons. The bill makes permanent: (1) certain housing assistance programs under the Homeless Assistance Act, and (2) the U.S. Interagency Council on Homelessness.