Aabar, that bought the company in July 2005, has sold it to Dubai-based GulfCap Group.
The sale was announced in July, but needed approval from Aabar's shareholders before it could proceed.
Dalma is based in Oman and operates 22 and drilling rigs in the Gulf, Algeria and India.
GulfCap was founded by investors from Saudi Arabia, Bahrain and Oman to invest in oil and gas, financial services and real estate ventures in Oman.
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