The seven men and six women cut a hole in a fence and chained themselves to railings on the north runway, beginning at around 3.30am on July 13 2015.
As the verdict was read out, one defendant shouted: "This is a farce!", as other gasped in disbelief.
District Judge Wright has told defendants they can expect jail sentences for their actions.
During their three-day trial at Willesden Magistrates' Court, defendants told of how they carried out the pre-planned action in order to 'save lives', using the defence of necessity.
The protesters claimed their actions were necessary and reasonable in order to reduce carbon emissions and halt climate change.
The court previously heard how Graham Edward James Thompson, 42, of Durlston Road, Hackney and a press officer for Greenpeace, explained that he was “compelled by his conscience” to take action that day.
Mr McGhee, prosecuting, said: “Why do you feel that your conscience entitles you to break the law?”
To which Mr Thompson replied: “In the context of this situation, breaking the law was not the most serious issue at hand.”
The 13 defendants all pleaded not guilty at Uxbridge Magistrates Court on August 19 2015.