Consolidations through takeovers and mergers are among the ways energy companies are seeking to reduce costs and become more efficient as oil prices have slumped.
A joint statement said the boards of both companies are recommending that shareholders approve the deal that will create a more competitive, stronger company for both sets of shareholders in today's volatile oil price world.
Shell said the takeover will add 25 per cent to its proved oil and gas reserves and 20 per cent to production compared with 2014, and boost its position in new oil and gas projects in Australia and Brazil.
"Bold, strategic moves shape our industry," Shell CEO Ben van Beurden said. "BG and Shell are a great fit. This transaction fits with our strategy and our read on the industry landscape around us."
The terms of the offer would result in BG shareholders owning about 19 per cent to the new combined business.
Shell said that bringing the two companies together would produce financial gains of about $2.5 billion a year.
Van Beurden said BG was a good fit for Shell looking to the future.
"The addition of BG's competitive natural gas positions makes strategic sense, ahead of the long-term growth in demand we see for this cleaner-burning fuel," he said.
BG's CEO Helge Lund said his company also would benefit from the takeover.
"BG's deep water positions and strengths in exploration, liquefaction, and LNG shipping and marketing will combine well with Shell's scale, development expertise and financial strength," he said.