The Labour-run council has issued £1.3m fines since August when traffic was banned from Coppergate and Lendal Bridge during the day.
Last week, a traffic adjudicator ruled the roads did not qualify because bus lanes and signage were inadequate.
But James Alexander, the leader of City of York Council, said "the principle of the trial" had been right.
Residents, tourists and businesses had complained about the restrictions from the outset.
Councillor Keith Aspden, Liberal Democrat leader, said: "It was a botched trial from the start which has made congestion worse and damaged local businesses."
In a statement on Monday night, Mr Alexander said lawyers had confirmed the implementation of the trial in August "was legal".
He denied its purpose had been to generate revenue, and said it had been aimed at reducing traffic over the bridge and through the city centre.
"It is clear, however, that the trial has been polarising and we need greater consensus amongst residents and businesses over measures to tackle congestion," Mr Alexander said.
He said he wanted an independently-chaired cross-party commission to look at the data and come up with more consensual suggestions for tackling congestion.

The American, 34, reached her 88th career final by beating Poland's Agnieszka Radwanska 6-4 7-6 (7-1).
It took 2012 champion Azarenka just over two hours to see off Karolina Pliskova, with the 26-year-old Belarusian winning 7-6 1-6 6-2.
"This year has been great. It feels so great to be supported," said Williams, twice a winner of the tournament.
"It's been a great comeback here in Indian Wells. I'm excited about that."
Williams won seven games in a row to take the first set and go 3-0 up in the second, before seven successive points clinched victory in the tie-break.
She has won 23 of her 24 matches at Indian Wells, taking a self-imposed 14-year exile from the event amidst allegations of racial abuse from fans after sister Venus withdrew minutes before their semi-final in 2001.
"I had a lot of support, I heard a lot of 'go Serenas' and that was kind of cool," added Williams, who won the tournament in 1999 and 2001.
Traffic restrictions on York's Lendal Bridge will be lifted on Saturday, the council has confirmed.
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World number one Serena Williams will face Victoria Azarenka in Sunday's BNP Paribas Open final at Indian Wells.