A huge cheer went up from Tahrir square where supporters of Mr. Morsi gathered.
Mr. Morsi defeated former Mubarak-era prime minister Ahmed Shafiq.
Egypt's election commission announced Sunday that Mr. Morsi won nearly 52 percent of the vote, beating Ahmed Shafiq. Mr. Morsi will become Egypt's first freely elected president.
The election commission was supposed to release the results Thursday, but it said it needed more time to investigate fraud allegations against both candidates.
Ahead of Sunday's announcement, officials deployed extra security forces to Cairo streets and key state institutions. Supporters of both Mr. Morsi and Mr. Shafiq had threatened a backlash should their candidate lose the closely contested election. So far though, there have been no reports of violence.
The Muslim Brotherhood is an international Islamist organization which calls for implementation of Sharia law, the separation of sexes, and the end of Western influences in the Middle East. It had promised violent protests if their candidate had not been declared the winner.