It follows a stormy week at the authority’s Woodhill House headquarters in which the ruling alliance lost four members, leaving it in the minority.
The 28-strong SNP group and the newly-formed Progressive Alliance held talks with the Democratic Independent and Green Group (DIGG) of Martin Ford and Paul Johnston, who have promised support on a confidence and supply basis.
Councillor Johnston said: “Our objective is a positive change in direction and it’s clear there is agreement on that.
“We are not entering a coalition. But we will give confidence and support for a stable Aberdeenshire going forward.”
SNP group leader Hamish Vernal said: “We’re delighted that after some intensive negotiations over the past few days, we have been able to reach an agreement with the Democratic Independent Group which reflects the broad and progressive policy consensus across our respective groups.
“It’s clear that together, we now have the numbers required to effect an orderly change of administration in Aberdeenshire and that’s what we aim to do.
“We’ll be taking advice from the chief executive in the days ahead on how best to now proceed.”
However, current council leader Jim Gifford questioned the legality of the agreement.
He said he had received advice that it did not constitute a group of 34 - the number needed for a majority.
The Mid-Formartine councillor added that it would be business as usual “until something happens to change that.”