The result indicates the vast majority of shareholders want the $27 billion (£20 billion) merger to proceed, despite the U.K.'s vote to leave the European Union (EU) last month.
This is the exchanges' third attempt to merge in 16 years. The bidding process saw Intercontinental Exchange (ICE ), the owner of New York Stock Exchange, consider a bid.
Deutsche Boerse shareholders have until July 12 to vote on the deal.
Concerns about the implications of Brexit on the merger have worried many. LSE attempted to sooth fears in a statement on Monday, in which it forecast the U.K. would remain a member of the EU for at least two years from now.
"Whether the U.K. is just European or a member of the EU, the merger will create a globally competitive, industry defining market infrastructure group at the service of European industry," it said in a statement after the shareholders' meeting.
An individual shareholder questioned the deal at the meeting, according to Reuters. Dinesh Jain said the LSE should abandon the merger, as it seemed "unlikely" Germany would approve it given the upcoming Brexit.
German market regulator BaFin has raised concerns about headquartering a euro zone exchange outside the EU.
"German regulators are uncomfortable with the idea that the base of operations will be situated in London and given that this deal was always about the lucrative clearing operations and euro-denominated derivatives, this deal could well find itself susceptible to further regulatory tweaking in the weeks and months ahead," Michael Hewson, chief markets analyst at CMC Markets, told CNBC via email.
However, another expert said BaFin might not be able to veto the deal.
"BaFin as such doesn't have a veto on the deal, but it does have a big say, being a big financial regulator in Germany. And you have seen the same concerns raised by many others, so the headquarter's location might be one of the big factors to look out at again," Gustav Sandstrom, a reporter at DealReporter, told CNBC on Monday.
The LSE said the potential merger of "equals" remained conditional on the agreement of other terms and the final approval by the boards, in a statement in March.
Under the terms of the deal, LSE shareholders would own 45.6 percent of the new holding company, while Deutsche Boerse would own 54.4 percent. The firms would continue to hold headquarters in London and Frankfurt, LSE has said.
Sandstrom said Brexit might actually work in favor of the merger.
"From the very beginning, they have said Brexit is not going to destroy the deal. It might make the deal even more compelling to have one leg in each — the U.K. and the EU," he told CNBC.