New deputy mayor Derek Hussey with his wife Karen at his recent installation at the Guilhdall earlier this month
The 25-1 vote follows growing pressure on Derek Hussey to resign over his drink driving convictions.
However, the vote is not binding.
Four councillors abstained from Thursday’s vote.
The UUP Deputy Mayor was the only councillor to vote against the Sinn Féin motion put forward by the party’s group leader on the council Sandra Duffy.
Mr Hussey said he intends to continue as deputy mayor.
However, Mr Hussey will stand down from his role as chair of the local Policing and Community Safety Partnership.
At the meeting on Thursday, councillors were read an email from Ulster Unionist Party leader Robin Swann confirming Mr Hussey would resign from the policing partnership role due to his increased workload as deputy mayor.
He will be replaced by party colleague Mary Hamilton.
The Deputy Mayor said he had received many messages of support in recent days despite growing calls for his resignation.
Earlier this week, the council’s Mayor, SDLP councillor John Boyle, met with two families whose loved ones were killed by drunk drivers.
The Gallagher and Bradley families had been calling for Mr Hussey to step down.
Tragic Martin Gallagher killed by death driver in 2009. Family want new Derry Deputy Mayor and convicted drink driver Derek Hussey to resign but he refuses
“My actions in the past we’re wrong and I have apologised for them,” Mr Hussey said on Thursday.
“I do not seek to cause hurt by seeking to retain my position as Deputy Mayor. It was not me who caused the fatalities of these families or any fatalities.”
Mr Hussey has three drink-driving convictions.
He was given a five-year driving ban and fined £800 in 2016 after pleading guilty.
The previous offences date back to 2004 and 2011.
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