The six-metre (20-foot) two-tonne bronze statue was a gift from Johannesburg with which Ramallah is twinned.
"I think that Nelson Mandela himself would have been extremely proud of what has been done today," Parks Tau, the mayor of the South African city, told AFP.
Palestinian president Mahmud Abbas also attended the ceremony at the renamed Nelson Mandela Square in the Al-Tireh district.
Mandela, who died in 2013, was South Africa's first president after the era of apartheid, a regime of segregation that the Palestinians accuse Israel of also imposing.
He was an ardent supporter of the Palestinian cause and a champion for Middle East peace.
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Ramallah several days ago installed huge posters celebrating the South African leader bearing his comment: "We know too well that our freedom is incomplete without the freedom of the Palestinians".
Ramallah mayor Mussa Hadid said the statue "symbolises the shared suffering" of the South African and Palestinian peoples.
During its journey to the pedestal in the West Bank, the statue was retained by Israeli customs for 30 days, as the Palestinian Authority does not control its own borders.
"Nelson Mandela, who had already spent 28 years in the jails of the apartheid regime in South Africa, was again detained for 30 days by the Israeli authorities," Hadid said.
Tau said Israeli customs had sought duty "equivalent to 10 times the price of the statue", but that this was not paid.
Hadid said the statue sent "a clear message to the Israeli coloniser and occupier -- that we are closer to freedom than you think".