The west London hub said it is confident it can keep charges - passed on to passengers in ticket prices - near existing rates despite the expansion project by delaying the building of a new terminal.
The Department for Transport has said it expects the industry to “drive down costs” and aim to keep charges “close to current levels”.
A Heathrow spokesman said: “We are confident that we can now meet that challenge.
“Effectively we’ll be able to expand the airport and passengers will continue paying what they pay today.
“It was key for the Government that this gets done affordably, but also it’s been a key issue for our airline partners as well.”
Heathrow’s half-year results show the airport increased turnover by 4.1% compared with the first six months of 2016, and recorded a profit after tax of £246 million.
Passenger numbers rose 3.9% to 37.1 million due to the use of larger, fuller aircraft.
Willie Walsh, the boss of British Airways’ parent company IAG, has repeatedly warned that expansion must be cheaper than the £17.6 billion budget estimated by the Government-commissioned Airports Commission.
He fears that landing fees could be raised and has insisted airlines “are not going to pay for inefficient expansion”.
Heathrow currently charges around £22 per passenger.
The airport said it has worked with carriers in a bid to develop an affordable strategy for building the third runway.
Although specific plans will not be released until a consultation is launched later this year, the airport is proposing to delay some of the more expensive aspects of the work.
Terminal capacity will initially be increased by modifying existing facilities rather than through new buildings.
The airport spokesman said: “It’s not necessarily that these things won’t be built.
“It’s just that we can do some clever things to add additional capacity to our existing terminals up front.
“We can get more passengers in to help spread the cost.”
The decision was welcomed by the Federation of Small Businesses, which claimed it could boost exports by lowering the costs to business users of accessing new and existing foreign markets.
The publication of the final Airports National Policy Statement setting out the Government’s position and a subsequent House of Commons vote is expected to take place in the first half of 2018.