Campaigners say losing their battle to prevent a new town from being built is "a bitter pill to swallow".
The 4,250-home Lubbesthorpe estate was approved at a meeting of Blaby District Council planners on Thursday.
More than 100 members of the public attended the ticket-only meeting, while others followed the proceedings online.
The reaction when the committee voted by 13 to four in favour of the scheme was stunned silence.
Paul Fox, secretary of the protest group Leicester Forest East Residents' Action Group, said Thursday's decision was a "bitter pill to swallow".
"I'm not at all surprised, but still extremely disappointed by the decision," he said.
"This part of Leicestershire is already too congested with traffic and air quality is far below EU standards.
"We have been let down and the abiding feeling is this was a done deal from the beginning."
Pete Jones, 47, of Braunstone Lane, Braunstone Town, said: "I left work the other day and it took 20 minutes to do the last 200 yards to get to my drive.
"This scheme is far too big and I don't think anyone has thought it through clearly."
Julien Birchall, of Leicester Forest West, said: "It's gridlock on the roads, so how they will cope with 10,000 more vehicles from this development I have no idea. It's an outrage."
More than 1,300 people objected to the 973-acre development on farm and woodland to the west of the M1. Three people said they were in favour. Other concerns included flooding and the loss of agricultural land.
Officers said the development would help Blaby meet its Government-set requirement for 8,500 more homes by 2029.
Planning officer Paul Tebbit said building in one place would minimise traffic growth.
But district councillor and former county council leader David Parsons said: "Most of the development in Blaby is being rammed into one quarter of the district and that is unacceptable."
Braunstone councillor Bill Wright, who voted against the plans, said: "I'm not against development by any means but not something of this size. I think it's crazy."
Croft Hill councillor David Freer said: "It was a very difficult decision. I don't like it but this development is needed."
The plans include investment in transport infrastructure, offices, schools and shops.
Paul Burton, of New Lubbesthorpe development consortium, said: "This decision will allow homes which are urgently required in Blaby, as well as a package of improvements."
It is now up to the Secretary of State to decide whether to hold a public inquiry.
If not, the council's approval will stand.
