The ceremony had been held up by a court petition filed by Mugabe's main rival, outgoing Prime Minister Morgan Tsvangirai, on allegations of electoral fraud, the BBC reported.
The Constitutional Court dismissed the case, saying Mugabe's re-election was "free, fair and credible."
Mugabe, of the Zanu-PF party, won with 61 percent of the vote to Tsvangirai's 34 percent in the July 31 presidential election.
Mugabe's re-election ended the frail power-sharing government formed by the two men in 2009 under pressure from regional leaders after the 2008 elections marred by violence and allegations of vote rigging.
Tsvangirai's Movement for Democratic Change lost two court challenges related to fraud claims in last month's elections. MDC officials alleged that more than 1 million voters were prevented from voting at polling stations, mostly in the capital and urban areas considered MDC strongholds.
MDC officials have indicated they are unwilling to maintain a partnership government with Zanu-PF. Tsvangirai had said he wouldn't attend the inauguration ceremony.
The United States said recently sanctions imposed on Mugabe and 119 other Zimbabwean individuals would remain in effect until more political reforms are implemented.