Bashir, who is wanted by the International Criminal Court on war crimes charges, won the elections with more than 94 percent of the vote.
The 71-year-old career soldier took the oath at the national assembly in Khartoum's twin city of Omdurman in front of members of parliament, military chiefs and foreign leaders and representatives, an AFP correspondent said.
Dressed in traditional gleaming white robes and a turban, a stern-looking Bashir made his vow on the Koran.
Bashir seized power in a 1989 Islamist-backed coup and won a 2010 election that was criticised for failing to meet international standards and was boycotted by the opposition.
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Ethnic insurgents launched a rebellion in the western region of Darfur in 2003 and Bashir government's unleashed the armed forces and allied militiamen.
More than 300,000 people have been killed in the conflict, the United Nations says, and more than two million displaced.
The ICC indicted Bashir in 2009 for alleged war crimes and crimes against humanity and in 2010 for genocide.