The electoral petition seeks an order for the result to be declared null and void and a new election to be called within 60 days.
The MDC’s 15 grounds include alleged bribery, abuse of “assisted voting” and manipulation of the electoral roll.
Robert Mugabe, 89, won with 61% of the presidential vote.
His Zanu-PF party gained a parliamentary majority of more than two-thirds, with 160 seats against 49 for the MDC.
The MDC is to file a complaint on the parliamentary results at a later date.
With a two-thirds majority, Zanu-PF is able to amend the constitution, potentially restoring presidential powers which were reduced earlier this year.
Lawyers for the MDC, which filed its petition with the country’s constitutional court, said they had “strong evidence of electoral irregularities”.
They said a shockingly high number of people were unable to vote at the polls, and that food and other bribes were used to persuade voters to back Robert Mugabe.
“The Movement of Democratic Change has filed its election petition… what we seek is that this election be declared null and void in terms of section 93 of the constitution of Zimbabwe,” said MDC spokesman Douglas Mwonzora.
The challenge comes a day after Zimbabwe’s electoral commission said nearly 305,000 voters had been turned away from polling stations on election day. The MDC says the true number is about 900,000.
Robert Mugabe’s margin of victory was some 940,000 votes.
A week after the election, Robert Mugabe dismissed criticism of the polls and lashed out at Western countries for their response.
Zimbabwe’s nine-member constitutional court has up to 14 days to respond to the legal challenge.
Correspondents say some of the judges are believed to be Mugabe loyalists.
The MDC says it is “aware” of this, and as a result it will make its appeal public and even produce evidence of “bribed goods”.
If the court upholds the results, Robert Mugabe must be sworn in within 48 hours of the ruling.
“We have done the best that we can under the circumstances, presented the matter before the court, and it is now up to the court to determine how strong the case is,” said MDC lawyer Chris Mhike.
African and regional monitors praised the poll for being peaceful but noted some irregularities. Western observers were not invited to witness the July 31 vote.
But a local observer group, the Zimbabwe Election Support Network (ZESN) and its network of 7,000 observers, has said that about one million voters – mainly in urban areas – were “systematically disenfranchised” by being omitted from the voters’ roll or turned away.
The electoral roll has come in for criticism for having duplicate names and the names of dead Zimbabweans.
The MDC says 900,000 people were turned away from polling stations – mostly in the capital where the MDC’s vote is strong – and another 300,000 people were coerced through “assisted voting”.
MDC leader Morgan Tsvangirai rejected the vote as fraudulent and said his party would boycott government institutions.
The Zanu-PF and the MDC have been in a coalition since 2009, after the last election sparked widespread violence.
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