Council leader Robert Light (Con) has been replaced by Mehboob Khan (Lab) who will lead a coalition with the Liberal Democrat group after a no confidence vote was carried.
Opposition councillors had been unhappy that the Tories proposed a referendum on school reforms in part of the area, giving residents an option which they said would cost£46m than had been budgeted for.
In a statement, Cllr Khan and his deputy, Kath Pinnock (Lib Dem) said their decision to take control of the council had not been taken in haste.
They said: “We strongly believe that the issues around the Building Schools for the Future programme in north Kirklees are of such significance for the future of local education and for the life chances of young people in Kirklees that we could no longer watch the former cabinet dither with yet another option and an ill thought through local referendum.”
They pledged to tackle low achievement across the borough and to ensure that every new school was viable.
In a posting on the conservativehome.com website, Cllr Light said: “Labour and the Liberal Democrats have decided they know better than parents do.
“We believe in democracy and wanted everyone to make their thoughts clear. We're sorry and disappointed that the other parties were more interested in political point-scoring than the future of children in Kirklees and we will now fight the new leaders all the way.”
Cllr Khan is one of the most senior Muslim councillors in Britain.