Earlier this month, the 23-year-old requested time away due to homesickness and family reasons.
McKenna thanked the club for its ongoing support.
“I want to thank the club for the continuous support they show both myself and my family,” McKenna said.
“I’m looking forward to returning to training in the coming days.”
General manager of football Dan Richardson said McKenna will commence training this week.
“Conor will return to Melbourne after spending time with his family in Ireland,” Richardson said.
“We remained in constant communication with Conor and his family, he continues to have our full support.
“We look forward to Conor returning to training mid this week alongside the entire squad following their short break.”