The decision will mean that pupils of Abronhill will merge with those at Cumbernauld High School after the 2013/14 school year.
They will all be taught at the Cumbernauld High School building until a new school is built adjacent to the current site.
The school featured in the 1981 hit romantic comedy directed by Bill Forsyth and starring John Gordon Sinclair and Clare Grogan.
Scott Campbell, a spokesman for the Save Abronhill High School campaign, said: "We are very disappointed by the decision taken.
"We are very angry that the councillors, who voted for the closure, didn't support the 'unprecedented response' of the community's rejection of the proposals, in the council's consultation."
"We believe that this decision is deeply flawed and that the council's main reasons for closing Abronhill High School are not sufficient enough to merit a closure."
Despite North Lanarkshire Council carrying out a six-week consultation and alternatives to closure suggested, campaigners believe no other options were given "serious consideration".
"We will now be taking our case to the Scottish Government to request a call-in on the decision. This fight isn't over yet," added Mr Campbell.
North Lanarkshire Council argues that both schools are no longer fit for modern schooling and are under-occupied. Additionally, the "rationalisation" of the two schools will result in a combined saving of £1.3 million.
Councillor Jim Logue, convener of learning and leisure services, said: "The fundamental reasons for making these proposals have not altered, namely, the schools are hugely under-occupied. Abronhill and Cumbernauld high schools alone are sitting with a combined surplus of around 950 empty places.
"We need to make savings to allow a new school to be built.
"We've listened to all the concerns raised and that's why we've given an extra year before the rationalisation will be implemented.
"We strongly believe that this decision will provide significant education benefits for pupils, in terms of greater flexibility and subject choice, a greatly improved learning environment and an enhanced school ethos."
He also said the decision will create a second state-of-the-art secondary school, the first being the new Greenfaulds High School campus, which will create an investment of £70 million for the area.
Local SNP MSP Jamie Hepburn called the decision "an absolute disgrace".
He said: "North Lanarkshire Council have once again put aside the wishes of the community in order to pursue their own agenda.
"The parents, pupils and wider community of Abronhill have run a tireless and excellent campaign to keep the school open. The arguments for Abronhill High School to remain open are as valid now as ever before, and the next step is to see if the Scottish Government will call this proposal in. I will be writing to them to make such a request shortly."
Councillors also agreed to close Calder Primary School and nursery class in Motherwell at the end of the school session 2012/13, with pupils transferring to either Muir Street Primary School or Glencairn Primary School from the start of school session 2013/14.