Goals from Joe Garner, Vimal Yoganathan and Joe Pritchard wrapped up an emphatic win for Mellon’s side at York.
They will face the winner of Wednesday’s second semi-final between Forest Green and Southend United.
It is the first time in 35 years that Oldham Athletic have reached a Wembley final and Mellon paid tribute to owner Frank Rothwell and his family, as well as chief executive Darren Royle and his family.
“I’m so pleased for the family that we can take them to Wembley, they’ve done so much for the football club,” Mellon added.
“We’ll give them that now but we’ll be going there to try to get Oldham back into the Football League.
“We know whoever we play against will be a difficult game but we’ll be ready to go.”
