He was addressing a crowd at Guildhall Square shortly after walking across the Peace Bridge with SDLP founder and past leader John Hume on Wednesday morning.
"You have to finish this, you have to be free, these children have to have a future," he said.
He added: "The most important thing is that you finish the job, that you free yourselves of the past so that you can embrace it and be proud of it and not be imprisoned by it."
Mr Clinton also used his speech to praise the role Mr Hume played in the NI peace process.
The former president continued: "Never underestimate the impact this small place has had on the large world because of that peace agreement.
"Since I left office I have been to well over 100 countries.
"I am frequently invited to go to places that are having problems to try and talk them through it and still people want to know - how was it done?"
Bill Clinton visited the north west city to launch a new book on peacemaking on behalf of the University of Ulster.
During the visit the university announced it has secured £3m in funding for a full-time academic position in its international conflict research unit to work on a new peace initiative.
The John Hume and Thomas P. O'Neill Chair in Peace will be based at the university's Magee Campus.
Earlier, John Hume said his visit to Derry is an "incredible honour" for the city.
Hume, who played an instrumental role in the 1998 Good Friday Agreement, said he holds "the greatest admiration" for the 42nd President of the United States.
The Nobel Laureate said: "I have known Bill Clinton for 22 years and I have met him every time I travelled to Washington, and I have always had the greatest admiration for him.
"I am deeply appreciative for all the work he has done to help Northern Ireland, in spite of all the difficulties during his time in the Oval Office.
"Bill Clinton had economic difficulties and international difficulties to deal with during his administration, yet he gave so much time to Northern Ireland and the peace process."
On Wednesday Mr Clinton also met with First Minister Peter Robinson and Deputy First Minister Martin McGuinness at Stormont Castle.
Ahead of his arrival, the 67-year-old had stressed the economic importance of developing a new generation of leaders.
Afterwards, Mr McGuinness told UTV: "I would class it as a very important meeting. It was a very positive, constructive meeting.
"Obviously given the fact that he spent something like an hour and a quarter with us [it's a] very clear indication along with his visits to Queen's University, the UU University of Ulster and the great accolade that he paid to John Hume and Pat today.
"[It's a] very clear indication of his intellectual, emotional attachment to a peace process that he heralds all over the world as one of the most successful."
He said that Mr Clinton's "finish the job" message at Derry's Guildhall couldn't be clearer.
The former US President later travelled to Belfast for the official opening of the new Queen's William J Clinton Leadership Institute on Wednesday night. The event was one of the first engagements for Queen's new vice-chancellor Professor Patrick Johnston.
He described the visit as "historic" for the university, adding: "The William J Clinton Leadership Institute symbolises our purpose: to create positive change in our society, to provide opportunity for individuals, organisations and institutions to grow and, in his words, helping to build creative networks of co-operation."
Mr Clinton was heavily involved in the peace process, especially in the run-up to the signing of the 1998 Good Friday Agreement.
He first visited Belfast in December 1995 and memorably performed the annual Christmas lights switch on at Belfast City Hall.