Officials from London and Edinburgh have been meeting for weeks to hammer out details of a vote on Scottish independence. Sticking points included the date and the wording of the question.
Cameron met Scottish First Minister Alex Salmond in Edinburgh to approve the deal, calling for a referendum before the end of 2014.
The prime minister is expected later to praise Scotland's two governments for coming together to deliver a "legal, fair and decisive" referendum that now puts the decision on a separate Scotland or a United Kingdom in the people's hands.
"This marks the beginning of an important chapter in Scotland's story and allows the real debate to begin," Cameron will say in a speech later Monday, according to prepared remarks released by his office.
Cameron and other pro-union politicians had pressed for the vote to be held earlier than 2014, because opinion polls show that only between a quarter and a third of Scots currently favor leaving the union.
Both sides claim they are confident of victory in the vote that will decide the constitutional future of the United Kingdom.
If Scotland does break away it will end more than 300 years of political union with England.