Talks are to take place next week between the Labour group and other parties after Thursday's election led to it securing the biggest number of seats at county level in Cumbria.
It's expected that a deal will be done ahead of the first full council meeting of the new administration on 16 May.
A new leader of the authority and details on the make up of the administration will have to be agreed.
Labour are the biggest party in the county with 35 seats; the Conservatives have 26 and the Liberal Democrats 16.
The remaining seven seats went to independents and other parties.