The proposals for a 500-space scheme with a bus link to Flemingate have been put forward by Vistry Group (Yorkshire) and Strata Homes as part of a wider housing development.
The intention is that the developers pay for the park and ride, which will then be transferred to East Riding Council.
A legal agreement issued with the outline planning consent requires 300 spaces to be ready when the 149th house on phase two is occupied.
The other 200 have to be available before the 234th house on phase two is occupied.
Opposition Liberal Democrats have argued that the scheme is taking far too long. Their alternative budget proposals earlier this year included using £4m in reserves to get started on the scheme.
Coun Linda Johnson said: “From our perspective this could have been done in lockdown.
"The pressure on parking in the town is increasing all the time with the demolition of the car park on Lord Roberts Road - they are only going to leave 100 spaces."
Consultation is ongoing about the part-pedestrianisation of Saturday Market, which will see the loss of another 22 parking spaces.