South Africa's main opposition party until now, the Democratic Alliance, draws most of its support from white and mixed-race voters.
Cope emerged after Thabo Mbeki resigned as president in September after a power struggle with ANC leader Jacob Zuma.
Many supporters of the new party were unhappy at the way in which Mr Mbeki was forced to step down.
The BBC's Peter Biles reports from Bloemfontein that delegates have been locked in feverish political debates.
They see the launch as a key moment that signals the growth and development of South Africa's young democracy, he says.
Mr Zuma is also in Bloemfontein on Tuesday for a party rally widely seen as an attempt to divert attention from the launch of Cope.
"It is a call to us, as former soldiers of [ANC's now-defunct military wing Umkhonto weSizwe] MK, to participate in today's battles, the battles that are more important, the battles of building a new nation, of developing South Africa," he said.
As it confirmed Mr Lekota as its leader, Cope named the former premier of Gauteng province, Mbhazima Shilowa, as its first deputy president.
The party also unveiled its latest high profile supporter, the anti-apartheid activist and cleric Allan Boesak.
Mr Boesak was given a rapturous welcome by Cope supporters, before telling them that the tide had turned against the ANC.
Mr Lekota, who has ruled out any reconciliation with the ANC, said that expanding the economy would be the linchpin of Cope's electoral campaign.
"We need to fight joblessness and grow our economy," he said.
"Our approach is stability, hard work and growth."
Mosiuoa Lekota addresses Cope supporters
South African analyst William Mervin Gumede told the BBC's Focus on Africa programme that Cope is already starting to change the country's politics.
"Cope has changed the ANC already - the ANC is trying to be more accountable, the ANC is trying to be more consultative and is going to the electorate to explain its decisions - something it hasn't done in the past."
The breakaway party's formation has been marked by a lengthy and problematic search for a name.
The ANC has laid claim to the Congress of the People, since it was the name used for a historic, ANC-sponsored event in 1955.
But the High Court ruled earlier this month that the new party could use the name.
1: South African National Congress, challenged by ANC as too similar to its name
2: South African Democratic Congress, already registered by another party
3: Congress of the People, refers to an event when the ANC's Freedom Charter was signed
Its first choice - South African National Congress - was challenged by the ANC, which said it was too similar to its own name.
Their second choice - South African Democratic Congress - was already registered as a party.
In its first electoral test earlier this month, the ANC dissidents won 10 of 27 wards in the Western Cape - the province where the ANC has always been least popular.
The Cope members had to stand as independent candidates because of the dispute over the party's name.
Our correspondent says the challenge for the new party is to distance itself from Mr Mbeki, and not appear like a group of embittered losers from last year's ANC national conference in Polokwane, where Mr Zuma defeated Mr Mbeki in a leadership contest.
But he also says that Cope, which says it has more than 400,000 members, is in a position to make serious inroads into ANC dominance.
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