Total will take over all decommissioning obligations now amounting to $2.9 billion and will maintain Maersk Oil's position in the North Sea with strong Copenhagen and Esbjerg bases.
In July, Total took over from Maersk Oil as operator of the giant Al Shaheen field, offshore Qatar.
AP Moller Maersk's share price rose 4 per cent in Monday trading, while Total's was down 0.1 per cent.
Total will pay for Maersk Oil with a mix of shares and debt takeover.
Under the deal, in which Total will also take on some $2.5bn worth of debt, the French company is paying in shares and will acquire a 3.75% stake in Maersk.
Total has proved more resilient than many other oil companies following the price slump that struck the industry from 2014, cutting costs faster and earlier, which is now allowing it to invest in new projects. "Some of Maersk North Sea technology can be useful in the Middle East, such as the tools for drilling and extracting from chalk areas", he said.More news: Gareth Bale shines in opening day Deportivo La Coruna win
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Denmark will become a regional hub for all Total's operations in Denmark, Norway and the Netherlands, based on Maersk Oil's capabilities and strong position in the North Sea region.
The deal is a vote of confidence in the North Sea, where around 80% of Maersk's reserves are located. Maersk had been considering spinning off the oil and gas assets in an initial public offering, but "we offered them another option".
Brent crude has risen 17.3 per cent from a 2017 low of $44.82 a barrel and traded at $52.56 at 10.38am Luxembourg time, according to Bloomberg data. "This deal demonstrates Total's purchasing power and free cash flow", said Mr Brenac.
The company said the deal would make Total the second-largest operator in the North Sea, with substantial operations in Britain, Norway and Denmark. The deal has been approved by both companies' boards but remains subject to shareholder votes and regulatory approvals. Neither TOTAL S.A. nor any of its subsidiaries assumes any obligation to update publicly any forward-looking information or statement, objectives or trends contained in this document whether as a result of new information, future events or otherwise.
"This may not be the final word from Total", he said.