He was the only candidate nominated by parliament, which is dominated by his African National Congress. MPs broke into song at the announcement.
In his first presidential speech, Mr Ramaphosa, 65, said he would tackle the corruption which allegedly became widespread under Mr Zuma.
The ANC had told Mr Zuma to step down or face a vote of no-confidence.
Mr Zuma faces numerous corruption allegations but denies any wrongdoing.
One allegation is that he allowed the wealthy Gupta family, who whom he has personal ties, to wield influence over policy, in an example of “state capture”.
An arrest warrant has been issued for Ajay Gupta, one of the three most prominent Gupta brothers, officials said on Thursday.
This follows a raid by the Hawks, an elite police unit, on their home on Wednesday. The family has denied corruption allegations.
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President Ramaphosa told parliament that corruption and state capture were “on our radar screen”.
He is due to deliver a State of the Nation address on Friday. This was delayed last week amid uncertainty about who should deliver it and Mr Zuma’s reluctance to step down.
One opposition party, the Economic Freedom Fighters, walked out of the parliamentary debate. It wants new elections, rather than the ANC deciding on the identity of the new president.