More than 80% of investor votes cast backed the takeover, while 17% were made against the deal.
BG shareholders will vote in London on Thursday and, if approved, the acquisition will complete on 15 February.
Ben van Beurden, chief executive of Shell, said: "I am delighted with the positive shareholder vote and the confidence that shareholders have shown in the strategic logic of the combination of Shell and BG."
There have been concerns over the rationale for the deal following the recent hefty falls in oil prices due to over-supply and falling demand as the world economy slows.
The cost of crude slumped below 28 US dollars a barrel at one stage last week and has collapsed by more than 70% since a peak of around 115 US dollars a barrel in the summer of 2014.
Shell has priced its BG acquisition based on oil prices rising sharply from their current low levels - predicting a bounce back of more than 35% this year and further rises next year.
London-listed Shell revealed the impact of the tumbling cost of crude last week when it warned earnings are expected to more than halve for 2015.
The group said it expects full-year underlying earnings to tumble to between 10.4 billion dollars (£7.3bn) and 10.7 billion dollars (£7.6bn).
This is slightly below expectations in the City and marks a sharp fall on the 22.56 billion dollars (£15.9bn) reported for 2014.
The slump in 2015 earnings comes after Shell said fourth quarter earnings are expected to nearly halve to between 1.6 billion US dollars (£1.1bn) and 1.9 billion US dollars (£1.3bn).
This is down from 3.26 billion US dollars (£2.3bn) a year earlier and slightly below analyst expectations.
In a move to appease worried investors, Shell confirmed in last week's update that shareholders will share out 27 billion US dollars (£19.1bn) in dividends for 2015 and 2016, with the group confirming payouts expected to total 1.88 US dollars (£1.33) a share for last year and at least the same for the year ahead if the BG deal completes.
Shell will report full-year results on 4 February.
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