The London Stock Exchange, which declined to comment earlier on Thursday about the Dubai deal, welcomed the Qatar investment.
It said it had a long-standing relationship with the Qatari investors based on plans to develop the market in Qatar.
A LSE statement said: "The exchange believes that, given the strength of Qatar's economy and the development of Doha as a major financial centre, there are significant opportunities to build further this relationship to the mutual benefit of both parties."
The QIA also announced that it had acquired 9.98 percent of OMX, the Nordic stock market operator.
Meanwhile, in a complicated agreement, Nasdaq completed a deal with Borse Dubai that will leave Nasdaq in overall control of OMX.
Borse Dubai will complete its $4bn takeover of OMX but will then sell all of its interest to Nasdaq.
In return, Borse Dubai will receive a 20% stake in Nasdaq and 28% of the LSE.
With a combined total of 48 per cent, Qatar and Dubai will own nearly half of the London exchange.
LSE shares soared 9.8 per cent to $32.03) on Thursday.