Plans include relocating the town's Central Library and cutting back on the Citizens Advice Bureau.
The council will also work with traders to find a private buyer for the town's Victorian indoor market.
The Labour-run authority said it was implementing the cuts "with a heavy heart" and blamed "severe austerity cuts imposed by central government".
Councillor Bill Dixon, leader of the authority, said that tough choices had been made, but local people had been able to comment during a public consultation.
"There were other cuts that people didn't want us to make," he said.
"Withdrawing school patrol crossings for example - some authorities have done that, this authority decided not to."
Responding to protesters opposed to the relocation of the Crown Street Library to the Dolphin Centre, he said:  "I was born and bred in the town.
"I do understand the attachment to Crown Street Library, but we should emphasise we are not closing the library but moving it."
Darlington Council has rubber stamped moves aimed at making £10m savings over the next four years.