The pledge comes ahead of a government decision expected this summer on whether to expand Heathrow or Gatwick, the BBC reported today.
Last year, the Davies Commission recommended expanding Heathrow, but with strict environmental restrictions.
Heathrow said it will allow a longer quiet period overnight, with flights not allowed to land between 11pm and 5:30am, from their current 11.30pm finish and 4.30am start.
The offer falls short of the recommendations made by Sir Howard Davies' inquiry, which wanted a ban on night flights between 11.30pm and 6.00am.
It supported the introduction of an independent noise authority and pledged not to add new capacity unless the airport complied with EU air quality limits.
In a letter to Prime Minister David Cameron, Heathrow's chief executive John Holland-Kaye said the planned expansion would provide a boost to the economy while balancing the impact on the environment.
"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.
"Expanding Heathrow can help Britain win thousands more jobs and ensure that future generations have the same economic opportunity that we have enjoyed," Holland-Kaye said.
The airport has pledged to create an ultra-low emissions zone for airport vehicles by 2025 and develop an emissions charging scheme for all vehicles accessing the airport.
Stewart Wingate, chief executive of Gatwick Airport, described announcement by Heathrow's owners as a "desperate last throw from a project that has repeatedly failed".
The Commons' Transport Select Committee published a report last week which urged ministers to set out a clear timetable for airport expansion.
The plan involves building a new 3,500m runway about two miles north of the two runways Heathrow already has at an estimated cost of 18.6 billion pounds.
Heathrow is the busiest airport in the UK, as well as the busiest airport in Europe by passenger traffic, and sixth busiest airport in the world by total passenger traffic. In 2015, it handled a record 75 million passengers.
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