The move effectively ends a bitter battle that started around nine months ago when DNO bought a stake in the British firm, only for Faroe to resist its requests for board seats.
DNO said on Wednesday it owned or had acceptances for its bid representing 52.44 percent of Faroe's share capital, up from 43.8 percent five days ago.
It raised the offer to 160 pence a share in cash on Tuesday from a 152 pence bid made in November that failed to convince enough Faroe investors to give it a majority.
Faroe rejected DNO's initial bid, which was accompanied by public criticism of the British firm's management and performance, as inadequate and opportunistic.
But Faroe said on Wednesday it would recommend DNO's improved offer to its shareholders.
DNO intends to delist North Sea operator Faroe from London's AIM stock exchange once it controls 75 percent of voting rights linked to Faroe shares.
Faroe, which operates in the Norwegian North Sea, expects to produce between 12,000 and 14,000 barrels per day in 2018, while DNO's output in the third quarter was around 81,500 barrels of oil equivalent on a company working interest basis.
RBC Markets analysts said DNO's improved offer represented "reasonable value in today's market" and offered shareholders an opportunity to exit Faroe and buy alternative London or Oslo-listed stocks at decent valuations.
"Having embarked on a hostile deal, DNO commenced a negative campaign which ... might have undermined its own investment case, and raised questions about its 'need' for asset diversification. Assuming completion of this deal, we believe that DNO needs to get on the front foot and talk up its business case," RBC said.
At 1028 GMT, Faroe shares were up 4.3 percent at 160.2 pence, while Oslo-listed DNO's stock was up 4.4 percent at 15 Norwegian crowns.
($1 = 0.7837 pounds)
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