Liberal Democrat Coun Denis Healy, of St Mary’s ward, said the plans were long overdue and followed several unsuccessful attempts from his party to bring them forward.
Coun Paul Nickerson, Conservative ward member for Minster and Woodmansey, said he and others also backed the plans despite earlier scepticism over its benefits and cost.
Their comments come as plans for the park and ride were unveiled last week following flooding and drainage studies in August.
Plans for the facility, north of Minster Way in Woodmansey, feature 500 parking spaces and a bus link to Beverley’s Flemingate Shopping Centre.
The park and ride has been subject to a long running political battle between the ruling Conservatives and opposition Liberal Democrats.
Plans were first set out in the council’s local development strategy, with housing developers set to meet the estimated £2.5m cost.
Liberal Democrats have previously pushed for the scheme to be brought forward by using money from council reserves which the developer would cover later.
But Conservatives, including those from Beverley wards, resisted the plans fearing local council taxpayers could be on the hook if developers could not meet the cost.
Coun Healy said plans were long overdue, dubbing an access road already built for the site a 'road to nowhere'.
The Liberal Democrat said: “Plans for a park and ride in Beverley have been in the stocks for five years, they were in the East Riding Local Plan.
“The benefits for Beverley are immeasurable, this will result in less pollution, better air quality and reduced congestion in the town centre, as well as alleviating pressure on existing parking spaces.
“The plans also come during the COP26 talks in Glasgow and they will help to reach carbon neutrality goals.
“Beverley’s also growing as a tourist destination, we’ve got people visiting at the weekend not only from Hull but from South and West Yorkshire.
“Some will say that it will not result in much more parking because of the part pedestrianisation of Saturday Market, but Liberal Democrats have always said that should go hand in hand with a park and ride. My only regret is that it hasn’t happened sooner.
“The Liberal Democrats have brought it up at council meetings four times in the last two years but Conservatives have blocked it. But we’re here now and I want to work with other councillors to get this over the line.
“Our argument was that funding should be brought forward from council reserves to kickstart the scheme, but ultimately it was always the developers who were going to pay.
“We spoke to council finance officers about it, it would have just been a paper exercise.
“The planning process will take a relatively long time, it will have to go to consultation so when the first spade will be dug remains to be seen.”
Coun Nickerson said he and other Conservative ward members were now prepared to back the plans after concluding the economic case stacked up.
The councillor said: “The park and ride will be a boost for tourism and a boost for jobs. We were right to be sceptical at first, but we’ve asked officers to look into the case for it and now we’re satisfied with it, it could bring tens of millions into the local economy in the coming years.
“It’s got the potential to help the economy and ease traffic, most major tourist destinations have park and rides which are well used.
“The Liberal Democrat plans would have left council taxpayers footing the bill for this, we’ve got a £12m budget deficit and money from our reserves has been used for coronavirus.
“The developer may not have stayed solvent, there would have been a risk that we never got the money back and we’ve said as a matter of principle that they should be the ones paying for this.”