This is part of Out-Law's series of news and insights from Pinsent Masons experts on the impact of the UK's EU referendum. Watch our video on the issues facing businesses and sign up to receive our 'What next?' checklist.
99.9% of LSE shareholders voting on the resolutions voted to approve the merger, the LSE said in a statement.
Deutsche Börse shareholders will vote on the deal on 12 July, and "regulators, politicians and unions in both the UK and Germany also will have their say" before the deal is finalised, the LSE said.
The exchange operators had agreed on the proposed £21 billion merger in February, and recommitted to the deal the day after the UK referendum, the LSE said.
A possible counterbid for the LSE from the owner of the New York stock exchange, Intercontinental Exchange, "never came to pass", the LSE said,
Mergers and acquisitions expert Jonathan Beastall, of Pinsent Masons, the law firm behind Out-Law.com said: "The overwhelming shareholder support in favour of the merger is a landmark moment for those watching public mergers and acquisition activity in the wake of Brexit."
It still has significant hurdles to pass, however, and "if the deal had gone off at this stage it would have spooked the markets", he said.
"M&A activity is likely to be subdued for a while, as it would be a brave chief executive who would instigate any new deal on the public markets now. But our experience is that transaction activity is still happening; while there has been an instant slowdown it has not been a shutdown. We have closed some deals post-Brexit and seen a number instigated. We are also seeing appetite from overseas investors who see opportunity as a result of the current weakness of Sterling," Beastall said.