"We believe in incremental reform, and that takes places in a peaceful and constitutional way. We reject violence and denounce it in all its forms," the new leader said.
Badie is the group's eighth supreme guide since it was founded in 1928.
Born in 1943 in the Nile Delta town of Mahalla el-Kubra, Badie was jailed for nine years in the 1960s after being accused of membership of a Brotherhood paramilitary cell that allegedly planned the overthrow of the government.
He later became responsible for ideological education in the group.
In the case for which Badie was jailed, thousands of Islamists were convicted and imprisoned while influential radical Islamist thinker Sayid Qutb was executed.
Although disowned by some Brotherhood members for his radical views, Badie and others in the movement continued to embrace Qutb, who advocated armed struggle to impose Islamic law.
Badie's election came after a bitter dispute between conservatives in the group, who place emphasis on strengthening the organisation and ideological outreach, and reformists advocating a more active public role.
Akef resigned in protest last year before the end of his term in office after conservative members of the Brotherhood politburo opposed a promotion for Essam Erian, who is associated with the group's reformist wing.
The conservative wing has been seen to consolidate its control in subsequent politburo elections, in which the group's deputy chief Muhammad Habib and reformist leader Abdel Moneim Abul-Futuh lost their seats.
Analysts say the new leadership team and a campaign of arrests by police are likely to encourage a shift away from public life. The government has also passed laws that make it harder to contest the 2011 parliament elections.