The Movement for Democratic Change (MDC) has accused the ruling ZANU-PF party and the election commission of ballot fraud in the July 30 vote, Zimbabwe's first poll since the ousting of Mugabe in November.
Former minister of education David Coltart added his voice to confirm the filing of the court papers to challenge the presidential results and some constituencies.
"We will rest when this country is liberated", Jameson Timba, the MDC's chief election agent, told journalists standing outside.
The Constitutional Court, which can declare a new victor or order a fresh election, must rule within 14 days of an election petition. "We have a good case and cause".
MDC must prove that any polling irregularities were widespread enough to change the outcome of the vote.
"There will not be any inauguration this Sunday until this matter has been resolved in the courts", said Chamisa's lawyer Thabani Mpofu said.
Judges could declare a victor, call another election, or order a run-off or recount, the Veritas legal group said.
The conduct of the election was largely deemed sound by worldwide monitors, but representatives of the European Union noted Mnangagwa benefited from an "un-level playing field" and some voter intimidation.
"On the basis of the evidence we have placed before the court, we seek in the main relief to the effect that the court should declare the proper victor and the proper victor is my client", Mpofu told reporters outside.
Worldwide monitors largely praised the conduct of the election itself, although European Union observers said that Mnangagwa, a former ally of Mugabe, benefited from an "un-level playing field" and a degree of voter intimidation.
"In the alternative, we seek that there be another election which complies with the dictates of the law", Mpofu said. "But if they want to meet us in court we have sufficient legal minds to meet them squarely in court".
The aftermath of the polls has been marred by allegations by rights groups as well as by the MDC of a crackdown on opposition members, including beatings and arrests.
The results of the presidential election were announced on Friday last week by the Zimbabwe Electoral Commission.