The former president described Martin McGuinness as a 'friend'
In a personal tribute to Mr McGuinness, he made an impassioned plea for leaders to finish the peace building process in Northern Ireland.
Mr Clinton had been central to the Good Friday Agreement negotiations in the 1990s.
Looking down at the coffin, which had been draped in an Irish Tricolour, he implored leaders to pick up where Mr McGuinness had left off.
In his eulogy, Mr Clinton said: "He persevered and he prevailed. He risked the wrath of his comrades and the rejection of his adversaries.
“He made honourable compromises and was strong enough to keep them and came to be trusted because his word was good.
“And he never stopped being who he was. A good husband, a good father, a follower of the faith of his father and mother and a passionate believer in a free, secure, self-governing Ireland.
"The only thing that happened was that he shrank the definition of 'us' and expanded the definition of 'them'."
Former US President Bill Clinton hugs Sinn Fein president Gerry Adams
Mr Clinton added: "Our friend earned this vast crowd today. Even more, he earned the right to ask us to honour his legacy by our living. To finish the work that is there to be done."
Thousands of people thronged the streets of Bogside as the funeral took place at the St Columba Church.
The former Deputy First Minister died on Tuesday from a rare heart condition, aged 66.
Mr McGuinness's beloved Bogside neighbourhood came to a standstill as his coffin was walked to the church, led by a lone piper.
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Martin McGuinness' life in pictures Tue, March 21, 2017
The former deputy first minister of Northern Ireland, has passed away aged 66
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Martin McGuinness and Tony Blair look on at Stormont Parliament Buildings in Belfast in 2007
Following his passionate eulogy, Mr Clinton spoke briefly with the McGuinness family and touched the coffin as he walked by.
During the slow procession to the church, his widow Bernie, as well as Sinn Fein president Gerry Adams and the party's leader at Stormont Michelle O'Neill, helped carry the coffin.
Attendees included Irish President Michael D Higgins and his predecessor, Mary McAleese, as well as Taoiseach Enda Kenny and former Taoiseach Bertie Ahern.
Former Democratic Unionist Stormont first ministers Peter Robinson and Arlene Foster were also among those attending Thursday's requiem mass.
Bill Clinton touched the coffin as he walked by
Mourners at the Derry service were told Mr McGuinness was a former IRA commander who became a mainstay of the peace process.
Although thousands of supporters have lauded his legacy, his death has drawn a very different response from many IRA victims, with some bereaved relatives not prepared to forgive him for his paramilitary past.