Isabel dos Santos, named by Forbes magazine as Africa’s richest woman, worth an estimated $3.3bn (£2.3bn), takes on the job after the entire board was sacked by her father in April.
Angola and Nigeria are Africa’s largest oil producers.
Critics accuse President dos Santos, who has ruled since 1979, of being increasingly authoritarian.
Ms Dos Santos has large stakes in many of Angola’s strategic industries, including diamonds, banking, media and telecommunications, with large parts of her business empire based in Portugal.
She owns 7% of the Portuguese oil and gas company Galp Energia.
A statement from her office said that she wanted to “ensure transparency” in the management of Songangol, and to improve the Angolan oil sector’s ability to compete globally.
Representatives for Ms Dos Santos deny that her wealth is largely due to her father’s position as president and has been acquired through state money and public funds.
Ms Dos Santos’ father is Africa’s second longest-serving leader, after Equatorial Guinea’s Teodoro Obiang Nguema Mbasogo.
In March, the 73-year-old said he was planning to step down in 2018, although he has failed to follow through on similar commitments made in the past.
Being head of the state oil company is “next to the presidency… the most powerful position in the country,” Angola analyst Aslak Orre told the BBC’s Newsday programme.
He said that many would see a possible political motive behind the appointment, especially given Mr Dos Santos’ age.
“The way he is channelling resources and public jobs to Isabel and his other children implies he is planning almost a monarchical succession… passing power from himself to one of his children.”
The president’s son Jose is already head of the country’s sovereign wealth fund, created to make investments using the country’s oil wealth.
The southern African state is also rich in diamonds, which fuelled a 27-year civil war in the country.
Angola witnessed an economic boom since the end of a civil war in 2002. However, critics of the elected government say the wealth has only benefited a small elite.
Child and maternal mortality rates are among the highest in the world.