The Danish company said in a statement it was bidding 57 Swedish crowns per share in cash for Sweden's Brostrom and that owners with 55.9 percent of Brostrom votes had undertaken to accept the offer.
"From the press release it looks like Brostrom is a sensible strategic match for Maersk Tankers," said Jacob Pedersen, analyst at Sydbank.
"I am sure that the increased volume in the product-tanker segment will be an advantage. It definitely improves the possibility to service multinational oil companies."
Brostrom's board recommended shareholders accept the offer, which it said represented a premium of 23.6 percent to the average share price over the last three months.
The board said in a statement that holders of all the company's A-shares had accepted the offer and had also tendered their B-shares. This represents 29.3 percent of Brostrom's share capital.