Helen Zille, former leader of South Africa’s main opposition Democratic Alliance (DA), has publicly apologised for her tweets saying there were some positive aspects of colonialism.
She said her comments in March were "insensitive to South Africans".
Ms Zille will step down from all party leadership positions but remain the premier of Western Cape province.
The row threatened the DA’s popularity, which is trying to extend its appeal among black people.
Party leader Mmusi Maimane said the deal will help DA focus on the 2019 general election.
He said the party chose to avoid a protracted legal battle and instead seek reconciliation.
Ms Zille had tweeted that colonialism was not only negative:
The comments caused public outrage forcing her to apologise at least three times with the DA bowing to political pressure to suspend her last week.
She said in an interview last week with BBC Focus on Africa that her comments on the legacy of colonialism were not any different to views expressed by among others, including former South African President Nelson Mandela and former Zambian leader Kenneth Kaunda.
She also said that similar views appear in textbooks used in South African schools.
Ms Zille said in the interview that her critics had to be consistent in their criticism and should not victimise her.
But today at a press conference with Mr Maimane she said she apologised "unreservedly".
Ms Zille read a prepared statement saying her comments were "indefensible" and "insensitive to South Africans who suffered from colonial oppression".
Helen Zille looked like a naughty school child sitting next to her headmaster as she apologised for her controversial tweets.
The apology and the deal that will see Ms Zille relinquish her party leadership positions has somewhat restored Mmusi Maimane’s authority as leader.
There is however no doubt that this controversy damaged the DA’s long-term project to unseat the governing African National Congress (ANC) in 2019.
Many black South Africans who backed the DA after becoming disillusioned with the troubled ANC felt offended by Ms Zille’s earlier attempt to defend the tweets.
The question is whether black DA voters, who were ridiculed for being subservient following Ms Zille’s tweets, will continue to support the party.
She also said she had "undermined" Mr Maimane saying that he is the leader of the party and "we must all get behind his leadership".
BBC’s Southern Africa correspondent Karen Allen reports that Ms Zille, who was a key figure in the anti-apartheid movement, has been accused by critics of damaging his leadership.
Mr Maimane said he found his colleague’s tweets offensive but added that she should continue with her government job - running the Western Cape Province.