The LibDem leader said people can be assured a No vote does not mean no change.
He said the Conference on a New Scotland, announced by Scottish Secretary Alistair Carmichael, would start work on delivering more powers and strengthening Scotland within the United Kingdom.
Speaking at a Road to the Referendum event, Mr Rennie said: "This referendum has sometimes been a divisive experience that has split the country, families and communities.
"It is important that we unite to maximise the oppor-tunities and deal construc-tively with the consequences of the result."
The Scottish party leader said the conference can heal the division created during the debate and focus on the future.
He added: "People can be confident that a No vote in September does not mean no change. Scottish Liberal Democrats were the first out of the blocks with Sir Menzies Campbell's plans for home rule in a federal UK.
"Since then Scottish Labour and the Scottish Conservatives have set out plans for more powers. And since then we have stood on a joint platform committing to deliver more powers in the event of a No vote some weeks from now."
Mr Rennie said he wanted to see money and ideas shared with people from the other UK countries working towards the LibDem idea of a federal UK.
He added: "Liberal Demo-crats will grasp the growing momentum for more powers to Scotland within the UK. With that we will guarantee change.
"Earlier this year I asked Sir Menzies Campbell to produce a second report - the Campbell II report - to set out a clear path for radical change in the event of a No vote. I accepted his recommendations in full."