The agreement brings an end to the past administration, which saw Labour and the Tories work together, with Labour councillors being suspended by the party as a result.
SNP councillor David Cameron will take on the mantle of lord provost - succeeding Labour's Barney Crockett - with Lib Dem Steve Delaney becoming deputy lord provost.
The SNP's Alex Nicoll and Lib Dem Ian Yuill are set to become co-leaders of the council.
The coalition has been formed despite Scottish Lib Dem leader Alex Cole-Hamilton expressing "significant anxieties" during the campaign about working with either the Tories or SNP.
But Mr Cole-Hamilton ultimately that said the decision would be made at a local level.
The Aberdeen branch of the Scottish Tories has blamed the Labour ban on formal coalitions for allowing the SNP into power in the city.
"Labour's ban on coalitions has meant that they've capitulated to the SNP," a tweet from the branch said.
"Their weakness means that a party that has repeatedly failed to stand up for Aberdeen will take the reigns of our city."