The Labour group on Aberdeen City Council this week called for all options to be explored to allow the authority to run its own bus company.
In 2013, Labour's Mr Young tweeted that only political lunatics would support similar plans.
Mr Young said the situation had now changed.
A motion on the plans has been tabled for discussion at a council meeting later this month.
Aberdeen South MP Callum McCaig was behind the proposal in 2013 when he was an SNP councillor.
He said: "I suggested an opportunity to establish a bus company owned and run by the city of Aberdeen for the benefit of the citizens of Aberdeen.
"But Willie Young on his favourite medium of Twitter said they had voted against it because only the politically insane would support it."
Mr Young said: "Four years ago I was absolutely right because four years ago the finances of the council were an absolute mess.
"We have managed to sort out our finances.
"There's now a need for a public bus service."
A councillor has defended a tweet in which he claimed setting up a publicly-owned bus firm in the city would be for "political lunatics".