LONDON — In one of the first energy mergers in the era of low prices, shareholders on Wednesday approved the acquisition of the , the Britain-based oil and gas producer, for about $50 billion.

Analysts had expected major oil companies like Shell and ExxonMobil to take advantage of to acquire rivals or smaller companies to strengthen their position, but there have been few big moves so far, perhaps because of the steepness of the drop in oil prices, which have fallen since the summer of 2014 to around $30 a barrel from more than $100 dollar a barrel.

Shell said that about 83 percent of the shareholders, who met in The Hague, approved the deal.

“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 ,” the Shell chief executive, Ben van Beurden, said in a statement on Wednesday.

Even before Shell and BG announced the deal in April, there had long been rumors of a combination of the two companies. BG is considered a prime target for Shell. Although it is a midsize oil company, BG is a leading player in liquefied , a fuel that is chilled to liquid form and transported on ships. The combined entity would be the world leader among listed companies in liquefied natural gas.

BG, which has a leading position in offshore Brazilian waters, also complements Shell’s experience in developing oil and gas fields on the ocean floor. Shell has been a leader in the deepwater of the Gulf of Mexico and Nigeria.

Some investors have been skeptical about Shell’s spending large sums of money for an oil and gas company while prices are weak. Mr. van Beurden said that this was an opportune time for the financially strong to make bold moves.

The argument appears to have persuaded the investment community to go along with the cash-and-shares deal, which was initially priced at about $70 billion but has slid to about $50 billion as Shell’s stock price has fallen, which has provided a hedge. BG Group shareholders are scheduled to vote on the merger, which is expected to close in mid-February, on Thursday.

Shell has said that the deal will make money when oil is around $60 a barrel, but some analysts say that, assuming it manages the BG acquisition astutely, Shell will come out ahead even if prices do not rebound as Shell expects. Mr. van Beurden says that the BG deal will be a springboard for remaking Shell.

Oswald Clint, an analyst at Bernstein Research in London, said that regardless of the price, BG should help Shell upgrade its overall portfolio and cut future capital expenditures. For instance, with the additional sources of liquefied natural gas in the United States and elsewhere, Shell will be able to adjust its shipping schedules to maximize the price it receives and to lower costs.

Shell should also be able to pick the cream of the two companies’ exploration portfolios, selling off assets with less profit potential and cutting costs.

Unless Shell is ruthless, however, it may not see big gains. Shell “needs to clean out the garage to make room for the Ferrari,” Mr. Clint wrote in an email.