His nomination was supported by a coalition of Independent, Green, Liberal Democrat and Labour councillors.
Cllr Cleaver said he was honoured to be elected Leader of the Council.
"It is a responsibility I intend to discharge with a fair and open mind, a full heart, and with great thoroughness," he said.
"The majority group is one in which I feel I can take great pride. Half of them are newly-elected councillors who have been elected because they have listed to their electorate and they come here with great energy and commitment.
"We also have many long-serving councillors whose wisdom and experience will be so important in moving this council forward."
The Deputy Leader of the Council is Cllr Ashley Baxter (IND, Market and West Deeping) who is also the Cabinet Member for Finance.
Other Cabinet Members are Cllr Paul Stokes (IND, Grantham Arnoldfield); Cllr Phil Dilks (IND, Deeping St James); Cllr Philip Knowles (IND, Bourne East); Cllr Rhea Rayside (LIB DEM, Stamford St George's); Cllr Rhys Baker (GREEN, Bourne Austerby) and Cllr Patsy Ellis (GREEN, Grantham St Vincent's) who will job-share in the role. Their portfolios are yet to be confirmed.
The Chairman for the 2023/24 civic year is Cllr Gloria Johnson (CON, Stamford St George's) and the Vice-Chairman is Cllr Paul Fellows (IND, Bourne Austerby).
A new committee structure has been agreed and chairmen and vice-chairmen were appointed at the annual meeting:
· Culture and Leisure Overview and Scrutiny Committee - chairman Cllr Paul Fellows (IND); vice-chairman Cllr James Denniston (IND)
· Housing Overview and Scrutiny Committee - chairman Cllr Virginia Moran (IND); vice-chairman Cllr Lee Steptoe (LAB)
· Rural and Communities Overview and Scrutiny Committee - chairman Cllr Nikki Manterfield (CON); vice-chairman Cllr Steve Cunnington (IND)
· Finance and Economic Overview and Scrutiny Committee - chairman Cllr Mark Whittington (CON); vice-chairman Cllr Bridget Ley (IND)
· Environment Overview and Scrutiny Committee - chairman Cllr Ian Selby (IND); vice-chairman Cllr Emma Baker (GREEN)
· Licensing Committee - chairman Cllr Pam Bosworth (CON); vice-chairman Cllr Elvis Stooke (IND)
· Planning Committee - chairman Cllr David Bellamy (CON); vice-chairman Cllr Charmaine Morgan (IND)
· Governance and Audit Committee - chairman Cllr Tim Harrison (IND); vice-chairman Cllr Paul Wood (IND)
· Standards Committee - chairman Cllr Harrish Bisnauthsing (LIB DEM); vice-chairman Cllr Sarah Trotter (CON)
· Employment Committee - chairman Cllr Anna Kelly (IND); vice-chairman Cllr Pam Byrd (IND)