There were fears the plan could have cost banks up to £100m a year
The Treasury has backed down over proposals which critics claimed could have jeopardised the future of Scottish banknotes.
UK ministers wanted to bring in measures aimed at improving financial stability and protecting depositors.
They would require banks to lodge funds with the Bank of England to cover the value of their notes seven days a week.
But a deal is understood to have been struck which will allow Scottish banks to continue printing their own notes.
It has been estimated that the proposed measures could have cost the banks which issue notes - the Bank of Scotland, Royal Bank of Scotland and Clydesdale - up to £100m a year.
First Minister Alex Salmond described the U-turn as a "victory for Scotland and its financial sector".
"This is great news," he said. "I'm delighted the Treasury have dropped their ludicrous proposals that threatened the very existence of Scottish banknotes.
"This is the second occasion they've turned to this issue, so let's hope they've finally learnt their lesson and never jeopardise our banknotes again.
"Although some concessions have been made, this is a substantial victory and, as such, we welcome it. All those who took part in the campaign deserve congratulations - their determination ensured success."
The move was welcomed by Scottish Labour finance spokesman Iain Gray, who said: "It is very good news and a sensible outcome for all concerned that Treasury and Scottish banks have ensured Scottish notes have been fully secured and Scottish banks will continue to issue their bank notes."