Among the assets Total is buying include a 49.99% stake in the Culzean gas field, around 145 miles to the east of Aberdeen, in which BP has a 32% stake. Shareholders could expect an extraordinary dividend, share buyback, or distribution of the Total shares Maersk will receive in the deal.
Total's shares fell modestly on Monday morning, with stocks trading down about 0.2%.
Maersk will retain an interest in the sector through 97.5 million shares in the French energy group, equal to approximately 3.76% of Total.
Total will pay for the deal with $4.95 billion in shares, while also taking on $2.5 billion in Maersk oil debt.
Today's acquisition is thought to be the biggest oil deal by Total since, under its old name of TotalFina, it acquired Elf Aquitaine, its French rival, for £33.7bn in 2000.
It also noted the price in terms of output was almost a third less than Shell sold its North Sea portfolio to Chrysaor earlier this year.
Alongside Maersk Oil's UK North Sea assets, Total will also take over its Danish and Norwegian operations.
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The acquisition will transform Total into the second-largest operator in the North Sea.
"Our future position as the regional hub for Total's operations in Denmark, Norway and the Netherlands, recognises Maersk Oil's status in the North Sea region". Crude oil prices remain stuck at about $50 a barrel - half the level three years ago - and some notable traders see the the outlook for 2018 weakening.
"It was time for us to do what a real oil and gas company would do in a period such as this when prices are lower and costs are down". "This deal demonstrates Total's purchasing power and free cash flow", said Mr Brenac.
The transaction is subject to regulatory approval from relevant authorities including the Danish Minister of Energy, Utilities and Climate and competition authorities as well as required consultation and notification processes with Total S.A.'s employee representatives.
Total CEO Patrick Pouyanne called the transaction an "exceptional opportunity". The Danish company's main shareholder, A.P. Moller Holding, could also get a board seat, that is very important to Maersk.
Total will take over Maersk Oil's entire organization, portfolio, obligations and rights with minimal pre-conditions.
"Total is acquiring a deep specialist in unlocking complex reservoirs and boosting recovery factors through enhanced oil recovery techniques", Dr Kretzschmar said.