A large crowd of demonstrators gathered outside County Hall in Beverley ahead of the planning committee meeting on Thursday.
But eight Tory East Riding councillors - with the exception of Wolds Weighton councillor David Rudd - voted in favour, with a total of four against.
Fiona Roberts, from the campaign group No Mega Prison At Full Sutton, said she feared the nearby village of Full Sutton would become a "prison fortress".
She said they would explore the possibility of a judicial review, but first would have to consider the cost.
She also claimed councillors may have come under "enormous pressure" from the Ministry of Justice, after Prime Minister Boris Johnson announced a prison was going to be built in early August.
She said: "Although not totally inaccurate because a smaller one did have outline planning permission, I still feel it may have added pressure on councillors.
"I think Full Sutton will take an enormous beating from this in terms of traffic, in terms of prisoners coming out on day release and in terms of homeless prisoners being released.
"I think traffic through these country lanes will be a real hazard. I believe lives are likely to be lost because of ambulances being held up in Stamford Bridge - I think it is a huge mistake.
The Category C jail will house up to 1,440 inmates and be built next door to HMP Full Sutton, a maximum security prison with a capacity of 608.
Outline planning permission was given in 2017 to a jail with 50 per cent fewer prisoners, which sparked just 52 objections.
However fears have grown over the impact on local infrastructure with concerns about traffic jams doubling on the bridge in nearby Stamford Bridge, used by holidaymakers to get to the coast.
The meeting also heard there were concerns that tens of thousands of litres of sewage would have to be tankered away as there was no room for an on-site treatment plant.
Independent councillor Phil Davison, who voted against, said with just 50 inmates more the new jail would be the second largest in Europe or the biggest in the UK.
His understanding was that just 18 prison staff currently came from Full Sutton, with the rest travelling from Wakefield, Leeds, Harrogate, Scarborough, Whitby and Durham.
However committee chairman Coun Gary McMaster said even if they refused because of the existing planning permission, the plans they would "go ahead ahead whether we like it or not."
If it went to appeal he said it "is very likely to be overturned and the council will lose the right to impose any conditions whatsoever and that worries me.
"We do not wish to lose whatever little grip we have."
The total number of staff and inmates at the new facility and the existing prison - as high as 3,300 - will be up to seven times greater than the village’s 470-strong population.
Humberside Police had also objected on the grounds that the new prison will push up crime rates, placing "significant additional demand" on the force.
The MoJ said the jail, which will employ 720 staff, will open in 2024.
Prisons Minister Lucy Frazer said: “The new jail at Full Sutton is the first milestone in our long-term plan to deliver 10,000 additional modern and efficient prison places.
“It will create and support hundreds of jobs, during construction and afterwards, and will be a major boost to the local economy.
“The prison will also provide a better environment to steer offenders away from crime – ultimately keeping the public safer and reducing the number of future victims.”