The billboard campaign, created by Warwick Worldwide in collaboration with 150 secondary school pupils and teachers, features the slogan "Some people are gay. Get over it!".
Seven complainants claimed that the ad was "inappropriate for display where it could be seen by children"; five objected that the ad was "particularly offensive to Christian and other groups"; and two objected that the ad was offensive because it discriminated against heterosexual people and implied that all heterosexuals were homophobic.
The Advertising Standards Authority said that although some people might disagree with the advertiser's approach, the ad did not contain any offensive language or imagery that was likely to cause offence, or particular offence to heterosexuals or religious groups.
It said that the ad did not imply that heterosexual people were homophobic and did not promote homosexuality as an attractive lifestyle choice and did not take advantage of issues arising from children's sexuality for political gain.
The 600 billboard panels, donated by Titan Outdoor Advertising, were displayed across the UK in February and the ads will be allowed to re-run later this year.
Ben Summerskill, Stonewall chief executive, said: "We're delighted at the ASA's decision. This was a carefully designed campaign which has had a significant impact. We've received supportive messages from teachers and young people across the country saying it has helped them raise the issue of homophobic bullying in their schools for the first time
"This sort of bullying, which blights the lives of young people, has festered in the past precisely because it has been invisible."
Stonewall campaigns to achieve equality and justice for lesbians, gay men and bisexuals.