The acquisition is a part of a $13.4bn deal signed in November 2015 between the firms.
As per the deal, Airgas shareholders will receive $143 per share in cash from Air Liquide for all outstanding shares of Airgas.
Air Liquide expects the combined businesses to generate over €20bn in annual sales as well as more than $300m of pre-tax cost.. It will also employ approximately 68,000 people.
Air Liquide chairman and CEO Benoit Potier said: "There is strong industrial and market logic to this acquisition, which ideally positions Air Liquide for future growth.
"The two businesses are highly complementary, and the transaction extends our customer base through a unique, multi-channel distribution network and a nationwide presence in the US."
Airgas will operate as a subsidiary of Air Liquide within the company’s US operations.
Air Liquide will now finalize sales of certain production and distribution assets of the combined company in order to settle the US Federal Trade Commission (FTC) charges.
The US FTC recently said that the merger deal would have harmed competition and led to higher prices in several US and regional markets.
