Scotland is set for more devolved powers following the no vote.
The Tory leader said the debate must now widen to the rest of the UK.
"Just as the people of Scotland will have more powers over their affairs, so it follows that the people of England, Wales and Northern Ireland must have a bigger say over theirs," he said.
With the results in from all 32 Scottish council areas, the "No" side polled 2,001,926, votes to 1,617,989 for "Yes" - 55% to 45%.
The prime minister is set to outline plans for Scotland to have draft legislation published on its power on tax, spending and welfare by January.
But he said the focus must also be on the rest of the UK and what each nation can expect in the future, including how funding is allocated from central government.
He said: "It is time for our United Kingdom to come together and to move forward.
"A vital part of that will be a balanced settlement - fair to people in Scotland, and importantly to everyone in England, Wales and Northern Ireland as well."
Mr Cameron added: "In Wales, there are plans to give the Welsh government and the assembly more powers and I want Wales to be at the heart of the debate on how to make our United Kingdom work for all our nations."
Deputy Prime Minister Nick Clegg added that "this referendum marks not only a new chapter for Scotland within the UK but also wider constitutional reform across the Union."
Analysis - David Cornock, BBC Wales parliamentary correspondent
A lot of negotiations have gone on behind the scenes to ensure the prime minister's statement is not just an Anglo-Scottish one.
Welsh Secretary Stephen Crabb has been pushing to ensure Wales is not left behind in what David Cameron is calling this "new settlement".
Mr Cameron said that just as Scotland will have more power over their affairs, it follows that England, Wales and Northern Ireland must have a bigger say over theirs.
We know that more tax powers for Wales are in the pipeline. What this suggests is that perhaps there will be more flexibility about those powers.
David Cameron says the "West Lothian question" - English votes for English laws - needs a decisive answer.
Why should Scottish MPs vote on English and Welsh issues when English and Welsh MPs cannot vote on Scottish devolved issues? And to a lesser extent it applies to Welsh MPs on England-only issues.
Former Welsh secretary William Hague will be drawing up proposals.
This is important in terms of Conservative Party management as there is an English backlash from English Conservative MPs who think the current settlement is unfair.
Some would say the only answer to the West Lothian question is not to ask it because nobody has managed to resolve the issue.
Labour would say that banning Scottish MPs from some votes in the House of Commons would create two classes of MPs.
Nobody has yet come up with a definitive, universally accepted, answer to the West Lothian question, but David Cameron thinks and hopes he can have one in the next few weeks.
Prime Minister David Cameron says Wales must have a bigger say over its affairs in the wake of the Scottish independence referendum.