In a statement issued Wednesday, Hagel said the Department of Defense "welcomes" the ruling and "will immediately begin the process of implementing the Supreme Court's decision in consultation with the Department of Justice and other executive branch agencies."
"The Department of Defense intends to make the same benefits available to all military spouses -- regardless of sexual orientation -- as soon as possible," Hagel said. "That is now the law, and it is the right thing to do.
"Today's ruling helps ensure that all men and women who serve this country can be treated fairly and equally, with the full dignity and respect they so richly deserve," he said.
The Defense Department issued a statement saying it will update identification card issuance and "applicable implementing guidance," the department's American Forces Press Service reported.
"We estimate that this process will take about 6-12 weeks," the statement said. "For civilian employees, the department will look to [the Office of Personnel Management] for guidance."
The statement said the Pentagon would extend "all benefits to same-sex spouses of military personnel that are currently extended to opposite-sex spouses, including medical, dental, interment at Arlington National Cemetery, and with-dependent Basic Allowance for Housing. The department will implement these benefit changes as soon as possible for same-sex spouses."
Policies governing burial at Arlington National Cemetery "will apply equally to same-sex and opposite-sex spouses," the Defense Department said.