Adam Paynter from the Lib Dems is the new leader following a secret ballot by councillors on Tuesday.
Independent councillor Julian German is to take on the role of deputy leader.
The Conservatives won the largest number of council seats with 46, while the Lib Dems won 37 and independents returned 30 in the local elections.
More on Cornwall Council's new administration and other news
Negotiations over who takes control of the council have been in progress since the election.
The Conservatives, as the largest party, had the first chance to try to form either a minority administration or a coalition but their proposal was unanimously rejected by the independent members.
Mr Paynter, former deputy leader, said his party would "seek to put people first" and "ensure that we deliver on the Cornwall Devolution Deal".
He added: "We will pledge to invest in excess of Â£200 million in building 1,000 council houses for fair rent. We will also extend the living wage foundations living wage, to all council contracts."
The council has been led by a coalition of Liberal Democrats and independents since 2013.
The Liberal Democrats and independent councillors have regained joint control of Cornwall Council following two weeks of uncertainty.