Their remains were found in a single grave in Coghalstown, County Meath, in the Republic of Ireland in June.
Mr McKee's sisters said they were glad that 43 years after his death they can bury him with their mother.
The Disappeared are victims murdered and secretly buried by republicans during the Northern Ireland conflict.
Kevin McKee and Seamus Wright were both IRA members who were abducted and murdered by the organisation in 1972.
Their bodies were found unexpectedly during a search for another of the Disappeared, Joe Lynskey.
After the official identification, Mr McKee's sisters, Maria and Philomena, told the BBC: "It is bittersweet news that our brother's remains have been identified.
"The news has hit us with the shock of reality, even though we were expecting it.
"We are so so glad that, after 43 years, he will now be buried with our mother who never recovered from his disappearance."
Over the past 16 years, the Independent Commission for the Location of Victims' Remains (ICLVR) has searched for 16 people who were officially listed as the Disappeared.
The remains of 12 of the victims have been recovered and formally identified to date.
In a joint statement, ICLVR commissioners, Sir Ken Bloomfield and Frank Murphy, said they had received the results from DNA samples.
"The results positively indicate that the remains are those of Seamus Wright and Kevin McKee," the statement said.
"Dr Brian Farrell, coroner for the City of Dublin, has accepted this as evidence of identification and will shortly authorise the release of the remains to the families."
Sinn FÃ©in leader Gerry Adams said the news would "bring an end to the uncertainty for the McKee and Wright families".
"I want to appeal again for anyone with any information on those remains still not found to bring that information forward to the families, to the commission or myself," he said.
Confirmation that bodies found in a bog were Disappeared victims Kevin McKee and Seamus Wright is "bittersweet news", the McKee family has said.