After a meeting of Ms Sturgeon’s Cabinet, her spokesman said the Scottish Government would invoke a “dispute resolution mechanism” through the Joint Ministerial Council (JMC), the body dealing with relations between the UK Government and devolved administrations.
The process will be outlined in a letter to be sent by Finance Secretary Derek Mackay to the Chief Secretary of the Treasury Liz Truss.
“As well as writing to the Treasury today it is likely the Scottish Government will be invoking the UK Government with a view to invoking the dispute resolution mechanism under the JMC process,” the spokesman said.
“Cabinet expressed its displeasure at the nature of the deal with the DUP, which would appear to be a gross breach of established principles of devolution.”
The SNP has argued that the £1 billion for Northern Ireland should mean Scotland getting £2.9 billion if the funds were distributed by the Barnett Formula.
The extra cash negotiated by the DUP will not be handed over via Barnett, but sees an increase in Northern Ireland’s block grant.
The Barnett Formula has been designed to ensure that if funding goes up in England, there are consequentials for the devolved nations.
Scottish secretary David Mundell previously told the BBC he would not support a funding deal “which deliberately sought to subvert the Barnett rules”.
Ms Sturgeon’s spokesman said: “In terms of Scottish Secretary’s position, it is for David Mundell to reconcile previous statements with what has happened. But on the face of it they are completely and fundamentally at odds. So really the Scottish Secretary has to make a public statement about how is previous statements can be squared with what has happened.”