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.
The MDC accuses Mr Mnangagwa's ruling ZANU-PF party of rigging the vote, the first poll since long-time president Robert Mugabe was ousted in November.
Cde Mnangagwa said inauguration processes were going ahead as planned for Sunday, but that could stop if the MDC-Alliance files its petition today challenging the presidential results announced by the Zimbabwe Electoral Commission (ZEC). If it does this successfully, the court could order a recount or nullify the result altogether.
Chamisa's legal team arrived at the Constitutional Court at the eleventh hour with members of the media having been in wait for at least half a day.
Two days after the vote, six people were killed in an army crackdown on protests against the victory by Mnangagwa's ruling ZANU-PF party, a reminder that Zimbabwe will struggle to fix its image as a nation known for repression and economic collapse.
Also on Friday, lawyers for senior opposition figure Tendai Biti asked judges to throw out charges against him over the protests against alleged election fraud, in a case raising further global concern about the new government.
The Zimbabwe elections body, ZEC, declared Mnangagwa victor of the hotly contested polls with 50.8% of valid votes cast. We have a good case and cause!
Mr Mnangagwa has appealed for peace and promised an independent investigation into the post-election violence.
The Court has ordered that Mr. Biti is to surrender passport & title deeds and report twice a week to police, not to interfere with witnesses or address political gatherings.
Despite the contentious election result, the state-owned Herald newspaper has reported that President-elect Emmerson Mnangwagwa will be inaugurated on Sunday, 12 August.
On Thursday, opposition figure Tendai Biti was detained by Zimbabwean police after Zambian authorities rejected his bid for asylum.