"IAG represents an excellent opportunity to further develop our Westwards strategy," Qatar Airways Chief Executive Akbar Al Baker said on Friday, referring to its aim of expanding in western markets.
Non-European shareholders of IAG including Qatar Airways are subject to an overall cap on ownership as a result of the requirement for EU airlines to be majority owned by EU shareholders.
Shares in IAG, which have risen by 44 percent in the last three months, were trading up 0.3 percent at 565.5 pence. They earlier reached 590 pence, the highest level since the group was formed four years ago.
Analyst Mark Irvine-Fortescue at brokerage Jefferies said Qatar's investment was a strong endorsement of IAG and the tie-up would create opportunities in southeast Asia, India and the Middle East, where Qatar has an extensive network.
He said huge capacity growth from Middle East carriers such as Qatar, Etihad Airways and Emirates was putting pressure on the hubs of Europe's carriers.
"This strategy could be seen as a defensive 'if you can't beat them, join them' move and should in time improve IAG's structural and competitive positioning, possibly at the expense of Air France and Lufthansa," he said.
IAG Chief Executive Willie Walsh said in a statement: "We will talk to them about what opportunities exist to work more closely together and further IAG's ambitions".
IAG, a leading transatlantic carrier, is trying to buy Irish airline Aer Lingus for $1.5 billion, a deal that will increase its take-off and landing slots at its full-to-capacity London Heathrow hub.
Qatar Airways, owned by the country's sovereign wealth fund, has competed with regional rivals Emirates and Etihad Airways to become major global carriers. Its visibility in Europe has been strengthened by a sponsorship deal with Spanish soccer club Barcelona.
It joined one world in 2013, becoming the first Gulf airline in enter into a global alliance, which allows airlines to team up via code-sharing agreements to boost the number of flights they offer.