Griffiths left the Conservative Party in 2021 to sit as an independent in North Northamptonshire, before joining Reform in December.
He now represents the Croyland and Swanspool ward, and was selected to lead his new party after a group meeting.
Edward McDonald, councillor for Gretton and Weldon, was chosen as his deputy.
Reform UK won 677 of about 1,600 seats contested at last week’s local elections.
Griffiths said: “We have an incredible team of councillors with professional experience from all walks of life.
“It’s the most experienced team I’ve ever worked with in my time in local government, and I am excited by what we can deliver for local people.”
Griffiths said what his party achieved was “incredible”, after it also won West Northamptonshire Council.
“From a standing start we now have full control of both Northamptonshire councils,” he added.
