The pledge has been signed by Prime Minister David Cameron, Ed Miliband and Nick Clegg, BBC reported.
The "Yes" campaign said a vote for independence in Thursday's referendum is the only way to guarantee Scotland gets the powers it needs.
The first part of the agreement promises "extensive new powers" for the Scottish Parliament "delivered by the process and to the timetable agreed" by the three parties.
The second says the leaders agree that "the UK exists to ensure opportunity and security for all by sharing our resources equitably".
The third "categorically states" that the final say on funding for the National Health Service (NHS) will lie with the Scottish government "because of the continuation of the Barnett allocation for resources, and the powers of the Scottish Parliament to raise revenue".
The Barnett formula is the method used to determine the distribution of public spending around the UK.
On Monday, Scotland's First Minister Alex Salmond met with pro-independence business leaders in Edinburgh, while Cameron made a speech in Aberdeen promising further devolution.
Cameron urged the Scots to reject independence and vote "no" in a last ditch bid to save the union that has lasted for more than three centuries.
In Oct 2012, British Prime Minister David Cameron and Scottish First Minister Alex Salmond signed the Edinburgh Agreement, allowing Scotland to hold an independence referendum on the question of "Should Scotland be an independent country?"
The vote is scheduled for Thursday.