The airport revealed the measure as part of a package designed to reduce the impact of expansion on the local community and the environment.
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It will support the introduction of an independent noise authority, and pledged not to add new capacity unless it can do so without delaying UK compliance with EU air quality limits.
The west London hub also revealed it would accept any Government decision to rule out building a fourth runway in the future.
In July last year the Airports Commission recommended that a third runway should be built at Heathrow alongside a "significant" package of measures to make Heathrow's expansion more acceptable to nearby residents.
Heathrow chief executive John Holland-Kaye has written to Prime Minister David Cameron claiming that expansion would provide a boost to the economy while balancing the impact on the environment.
The letter stated: "You set up the Airports Commission and it unanimously recommended expanding Heathrow. You demanded ambitious plans from my team to deliver expansion with a bold and fair deal for our neighbours.
"Today, I am proud to submit a comprehensive plan that meets and exceeds your demands. This is a big commitment from us, but it is the right choice for the country, local communities and jobs across Britain.
"We have acted now to let you and your government make the right choice, in the long-term interest of our country. It will enable you to choose Heathrow and secure a stronger economy and Britain's place in the world.
"Expanding Heathrow can help Britain win thousands more jobs and ensure that future generations have the same economic opportunity that we have enjoyed."