The airport today released its submission to the Davies Commission, which is examining Britain's future airport capacity.
The three options are for a third runway at Heathrow, with the report suggesting a fourth runway would not be needed until at least 2040.
Heathrow claims the options are quicker and cheaper than any rival hub option, delivering extra capacity by 2025-29 and for between £14-18bn.
Heathrow believes the two westerly options - one to the north of the existing runways, one to the south - offer clear advantages.
The airport says they deliver a full-length third runway while minimising the impact on the local community from noise and compulsory house purchases.
The north west option performs better on noise and residential property impact than the north option - the only option east of the airport - while costing slightly more and taking slightly longer to build.
The south west option 'further improves' the situation for local residents but increases the cost, timescale and construction complexity.
The north option is the quickest and cheapest, but offers the least noise benefits and has the biggest residential property impact.
Colin Matthews, Heathrow's chief executive, said: "After half a century of vigorous debate, but little action, it is clear the UK desperately needs a single hub airport with the capacity to provide the links to emerging economies which can boost UK jobs, GDP and trade.
"It is clear that the best solution for taxpayers, passengers and business is to build on the strength we already have at Heathrow."
The north west option would be built just south of the M4/M25 junction and finish close to the north-east of Colnbrook.
The south-west option would run over the King George VI and Wraysbury Reservoirs, running over Staines Road out of Wraysbury.