Dave Stewart was voted in on Wednesday, following the resignation of Independent Jonathan Bacon on Monday.
Mr Stewart's executive also includes five fellow Conservatives, including new deputy leader Stuart Hutchinson.
The cross-party appointments will remain in place until the local council elections in May.
Mr Bacon and his deputy Steve Stubbings stood down on Monday claiming the "damaging behaviour" of Isle of Wight councillors was "overwhelming" efforts to deal with government cuts.
The authority needs to plug a Â£7.5m funding gap.
The full council is due to meet on 22 February to set the budget for 2017-18.
Mr Stewart said: "Yesterday we had a very productive and enlightening meeting with council officers about the budget - as a result, I am confident that we will be able to lead the council to achieve our primary objective of setting a legal and balanced budget for next year."
The new executive appointments are:
Isle of Wight Council's new Conservative leader has announced his executive, including a UKIP councillor and three Independents.