The two-term leader made the remarks last night during an hour-long address to a host of some of the most prestigious business leaders in Scotland at the Scottish Business Awards in Edinburgh.
Mr Clinton admitted he did not know enough about the domestic constitutional debate in Scotland but said he wanted to give his opinion.
The Democrat said he has top-level experience from other states around the world about what can happen when a country looks to split up.
He said: “You will come out of this better, regardless, if you go about it in the right way.
“It’s really important that there be an honest effort to list the consequences of this vote, one way or another.
“And then people that believe they are now, and might be on different sides, actually sit down and talk to each other about it.”
People have to treat each other with respect throughout the decision process, he urged.
He said: “When you get a question like this, how you respond to it, and how respectfully you treat it, and how honestly you try to listen to other people and then come to the practical conclusion, is sometimes as important as the decision that’s made,” he said.
“This place already has a quite clearly defined identity.
“You just have to run up the pluses and minuses and do it in a way that doesn’t tear the place apart while you’re trying to reach an agreement.”
Around 1,400 business representatives and other leading figures, including First Minister Alex Salmond, businessman Tom Hunter and entrepreneur Michelle Mone, attended the event at the Edinburgh International Conference Centre.
Mr Clinton agreed to appear at the glittering awards ceremony where he delivered a speech – Embracing Our Common Humanity – earlier this year after an invite went out from an Edinburgh sandwich shop owner.
The 66-year-old’s address to the ceremony came after months of painstaking work on the part of Josh Littlejohn, who organises the event and runs an acclaimed socially-conscious sandwich shop.
Mr Littlejohn, 26, has told how “delighted” he was to have landed such a heavyweight name. He said: “It’s great for the profile of the Scottish Business Awards.”
Earlier in the day the former president, who travels with a Secret Service protection unit, is understood to have played a round of golf in St Andrews.
Mr Clinton last visited Scotland in 2006 when he gave a speech about the dangers of global warming.