The 60-year-old engineer took 24% of vote in the first round of the election in May, with second place going to Ahmed Shafiq, a former air force chief who served briefly as former President Hosni Mubarak's last prime minister.
In the run-off, he took 51.73% of the vote.
Mr Mursi promises to bring "stability security, justice and prosperity" after a year of political upheaval.
He has said that it is time to put into practice the Brotherhood's famous slogan - "Islam is the solution" - and described its policy plans as having "a moderate Islamic reference".
Mr Mursi handed in his nomination papers for the presidential race on the last possible day after it emerged that Khairat al-Shater, a millionaire businessman and deputy leader of the Brotherhood, might be prevented from running.