Formed in 1997, BG is one of the two demerged companies of British Gas, and is engaged in exploration and production activitie. The company has a workforce of 5,200 across its operations, in 24 countries worldwide.
Under the recommended cash and share offer, Shell will pay approximately $20 per BG share, which is a premium of around 52% percent to the 90-day trading average.
The merger will create an entity worth $296bn that is expected to generate pre-tax synergies of approximately $2.5bn a year.
BG shareholders will own a 19% stake in the combined company, and will receive dividends of $1.88 per ordinary share in 2015, and at least that amount in 2016.
Shell chairman Jorma Ollila said: "This is an important transaction for Shell, accelerating the delivery of our strategy for shareholders.
"The result will be a more competitive, stronger company for both sets of shareholders in today’s volatile oil price world."
With this acquisition, Shell expects to increase its proved oil and gas reserves by 25%, and production capacities by 20%.
The Anglo-Dutch firm also expects the deal to strengthen its presence in new oil and gas projects, particularly in Australia LNG and Brazil deep water.
Shell CEO Ben van Beurden said: "This transaction will be a springboard for a faster rate of portfolio change, particularly in exploration and other long term plays.
"We will be concentrating on fewer themes, and at a larger scale, to drive profitability and balance risk, and unlock more value from the combined portfolios."
The company intends to launch a share buyback programme in 2017 of at least $25bn for the period of 2017 to 2020.
Shell also plans to increase its asset sales to $30bn between 2016 and 2018, in addition to planned £10bn spending cuts over three years in response to falling global oil prices.