The deal is the largest permitted by UK takeover rules, which set a maximum purchase of 15% in a week and 30% in six months without the permission of the target company.
This permission is unlikely to be granted. In a statement, the LSE said that it had "extremely strong growth prospects as a standalone business", and added that it did not believe that the current share price was high enough. A planned £510 million payout to shareholders will go ahead.
An earlier approach by Nasdaq for a takeover of the exchange was rebuffed last month by the LSE's management, which said that the bid undervalued the business.
The move could give Nasdaq a foothold in the consolidating European market. The three main players – LSE, Euronext and Deutsche Börse – are expected to consolidate in some way, but the shape of any tie up remains uncertain.
Deutsche Börse also attempted a bid for the LSE, a move that led to a shareholder revolt and the downfall of its chief executive, Werner Seifert. The shareholders involved, led by the hedge funds Atticus Capital and TCI, are believed to prefer a Deutsche/Euronext merger.
Nasdaq bought Threadneedle Asset Management, previously the LSE's largest single shareholder with 13.9% of the stock, and added another 1.1% of stock from other shareholders. The total holding is worth £444.7 million at the current price of 1,175 pence per share, Nasdaq said.