Coun Owen, East Wolds and Coastal ward member and deputy to previous council leader Steve Parnaby was elected at Wednesday's AGM.
His deputy is Counr John Holtby, of Mid Holderness ward, who replaced Coun Mike Stathers at their yearly party meeting.
It follows the ruling Conservative group becoming strained by divisions in recent months.
Group sources and others on the council said some Conservatives lacked confidence in Coun Burton’s ability to handle ongoing wrangling over a combined authority devolution deal with Hull.
The expulsion of Conservative Coun Paul Lisseter in the wake of a Planning Inspectorate ruling overturning the refusal of hundreds of homes in Pocklington and Swanland has also caused tension.
The handling of the fallout from Ofsted’s inadequate rating of council children’s services in March 2020 is also understood to have fuelled the fracture.
Conservative councillors are said to be dissatisfied with the leadership’s decision to stand by Children and Young People portfolio holder Coun Julie Abraham who remains in post after the rating.
Allegations of false claims from former Conservative Police and Crime Commissioner candidate Craig Ulliott over his time in Humberside Police dogged the party days into local elections campaigns.
Conservative Group rules state that whoever is leader of group will be supported for leader of the council.
Coun Lisseter said he had backed Coun Owen and before his suspension had offered to propose him and support him in this year's election campaign.
He said: "I think the Conservative Group needed a change of approach, simple as that. I think we will see some new faces coming to the fore in key positions to move the council forwards."