Thousands of people thronged the streets of Derry’s Bogside as the veteran Sinn Féin figure’s funeral took place in St Columba’s Church.
Mr McGuinness died on Tuesday from a rare heart condition aged 66.
Mr Clinton and ex-Democratic Unionist Stormont first ministers Peter Robinson and Arlene Foster were among those attending the requiem mass.
Looking down on a coffin draped in a Tricolour, the former US president, who was central to the Good Friday Agreement negotiations, implored today’s leaders to pick up where Mr McGuinness left off.
“He persevered and he prevailed. He risked the wrath of his comrades and the rejection of his adversaries,” Mr Clinton said.
“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 expanded the definition of ‘us’ and shrank the definition of ‘them’.
“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.”Mr Clinton spoke briefly with the McGuinness family after his passionate eulogy and touched the coffin as he walked by.
Mr McGuinness’s beloved Bogside neighbourhood came to a standstill as his coffin was walked to St Columba’s Church, led by a lone piper.
President Michael D Higgins and his predecessor, Mary McAleese, also attended, as did Taoiseach Enda Kenny and former taoiseach Bertie Ahern.
After the service, thousands followed the coffin of Mr McGuinness onward to the republican plot of the city cemetery.
Elected members of Sinn Féin formed a guard of honour as he was carried on his final journey.
Bishop Donal McKeown, Bishop of Derry, opened requiem Mass by welcoming dignitaries, public figures and politicians from Ireland, Britain, and the US.
He then turned to the McGuinness family and said: “For you, this is not the funeral of a public figure.
“This is a funeral of a husband, father, and a grandfather and our first thoughts are inevitably with you.”
Bishop McKeown noted the applause inside St Columba’s when some politicians had arrived ahead of Mr McGuinness’s remains, including for Ms Foster.
He also thanked those who had been involved in securing the Good Friday Agreement who travelled for the Mass, including from within the North, the Republic, Britain and the US.
“It’s a tribute to those who didn’t just talk the talk but walked the walk of implementing the Good Friday Agreement that all three of those strands are so well represented here,” Bishop McKeown told mourners.
Chief celebrant Fr Michael Canny began his homily by asking mourners to join him in sharing thoughts and prayers with the people of London following Wednesday’s terror attack.
He recalled the many tributes made to the Sinn Féin politician since his death and said Mr McGuinness spent year after year moving the community towards peace.
“There are people in this church today whose presence would have been unthinkable only a generation ago,” said Fr Canny.
The congregation heard that the presence of Mr McGuinness’s political rivals and opponents at the mass is “the most eloquent testimony” to his memory.
“When you seek his monument, look around you. You, by your presence, are his monument,” Fr Canny said.
He recalled conversations with Mr McGuinness in which the Sinn Féin veteran said he knew only too well how many people struggled with his IRA past.
“Republicans were not blameless, and many people right across the community find it difficult to forgive and impossible to forget,” he said. “By any standards, Martin McGuinness was a remarkable man and his life was a remarkable journey. The values he had, the principles he championed, are still very much alive.
“On that journey many years ago, Martin realised that the time for peace had come and he pursued the peace process with relentless energy for the rest of his days, until illness finally struck him down.
“In the course of that journey he encountered many obstacles but he remained resolute. In conversation, he often repeated that there was no other way, we had to continually work for the building of peace and a better future for all.
“Despite many setbacks, he never became disheartened.”