WASHINGTON — The Defense Department announced Wednesday that it would begin offering benefits to the same-sex spouses of military personnel and other employees by early September, in response to the Supreme Court decision that struck down the Defense of Marriage Act.

Under the plan, spousal and family benefits — including health care coverage, housing allowances and survivor benefits — will be available to all legally married military spouses. The same-sex spouses of service members and civilian Defense Department employees can claim the entitlements retroactively, starting with the date of the decision.

“The Department of Defense remains committed to ensuring that all men and women who serve in the U.S. military, and their families, are treated fairly and equally,” Defense Secretary Chuck Hagel wrote in a memo released by the Pentagon.

To be eligible, couples must provide a marriage certificate “that is valid in the place of celebration.” The Pentagon said it would grant leave to those who need to travel to a jurisdiction where same-sex marriage is recognized by law in order to get married. Thirteen states and the District of Columbia have legalized same-sex marriage.