The council chose to resolve the tie by drawing the name of the chair-to-be from a hat.
Regional council chief executive Chris McLay drew Storey's name from the hat and Storey drew Clarkson's name.
There were no hard feelings from Kneebone who immediately offered his congratulations and "full support" to Storey as the new chairwoman.
During the meeting, Storey said all councillors had "collectively been put here to represent our diverse communities and make good, robust decisions on behalf of the region".
"Our views and politics will inevitably differ ... but we all bring unique skills and experience to our roles here and collectively we are at a point in time where we can really make a lasting difference for the Waikato," Storey said.
Prior to the meeting where the council appointed its new chair, the elected members attended a pōwhiri to celebrate and welcome the new council.
Kaumātua representing local hapū guided the pōwhiri, which was attended by Tumuaki o te Kiingitanga (kingmaker) Hone Thompson.
At the pōwhiri, Kneebone performed the kaikōrero manuhiri, answering the karanga of kaumātua.