The Nasdaq Stock Market has signed a complex deal with Borse Dubai that will leave Nasdaq owning the Nordic stock market operator OMX.
OMX is based in Stockholm and runs a number of Nordic Exchanges
Borse Dubai will proceed with its $4bn (£2bn) takeover of OMX but will then sell all of the shares to Nasdaq.
In return, Borse Dubai will receive a 20% stake in Nasdaq and 28% of the London Stock Exchange (LSE).
Also on Thursday, the Gulf state of Qatar announced that it had bought a 20% stake in the LSE.
The Qatar Investment Authority said it was a long-term investment but that it did not intend to make an offer for the whole of the LSE unless another company did so first.
OMX operate stock markets in Iceland, Copenhagen and Helsinki as well as Stockholm, which is where it is based.
The deal resolves a takeover battle for OMX between Nasdaq and Borse Dubai.
A $4bn offer from Dubai had trumped an earlier $3.7bn recommended offer from Nasdaq.
The deal will have to be approved by shareholders and regulators in Europe and the US.
Nasdaq announced last month that it was going to sell some of its 31% stake in the London Stock Exchange after shareholders rejected its takeover offer for the UK exchange in February.