"We believe our proposed co-operation is an important step towards ensuring that we can compete effectively with rival alliances and manage through the challenges of record fuel prices and growing economic concerns," said Gerard Arpey, chairman and chief executive of AMR Corp, the parent company of American Airlines.
However, BA's rival Virgin Atlantic, owned by Sir Richard Branson, said the plan would reduce competition in the airline industry.
"What they're proposing is to create the world's biggest airline with American Airlines," said Virgin's Paul Charles.
"But we know what dominant players do - they snuff out competition, they raise prices and they become even more dominant."
Peter Morris, an aviation analyst from Ascend, told BBC News that it was unlikely that the deal would be anti-competitive.
"I think BA would argue that it will reduce its cost structure, which it can then pass on, to a degree, to passengers.
"BA is far less dominant than any of Air France, KLM or Lufthansa are out of their hubs."
The airlines hope the alliance will help them to cut costs
Mark Pritchard MP, a member of the House of Commons Transport Select Committee, also saw the decision as "good news" for both UK and US consumers.
"With tougher trading conditions for most airlines - coupled with the need to support the spirit of the Open Skies Agreement, Congress has no real excuse to delay the deal unnecessarily," he said.
The airlines said they planned to apply to the US Department of Transportation for immunity from US anti-competition rules and they would also notify European regulators.
They have previously failed to win an exemption from these laws because of their dominance at Heathrow, where BA and AA control nearly half of all the landing and take-off slots to the US from the airport.
However, BA chief executive Willie Walsh said the relationship would strengthen competition by providing consumers with easier journeys to more destinations.
"This may not be good news for Richard Branson but it is good news for consumers," Mr Walsh told the BBC.
Earlier this week, Sir Richard said he had written to presidential hopefuls Barack Obama and John McCain to warn that the proposed alliance between BA and American Airlines would severely damage competition on transatlantic routes.
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