We show that activation of Wnt/β-catenin and attenuation of Bmp signals, by combined gain- and loss-of-function mutations of β-catenin and Bmpr1a, respectively, results in rapidly growing, aggressive squamous cell carcinomas (SCC) in the salivary glands of mice. Tumours contain transplantable and hyperproliferative tumour propagating cells, which can be enriched by fluorescence activated cell sorting (FACS). Single mutations stimulate stem cells, but tumours are not formed. We show that β-catenin, CBP and Mll promote self-renewal and H3K4 tri-methylation in tumour propagating cells. Blocking β-catenin–CBP interaction with the small molecule ICG-001 and small-interfering RNAs against β-catenin, CBP or Mll abrogate hyperproliferation and H3K4 tri-methylation, and induce differentiation of cultured tumour propagating cells into acini-like structures. ICG-001 decreases H3K4me3 at promoters of stem cell-associated genes in vitro and reduces tumour growth in vivo. Remarkably, high Wnt/β-catenin and low Bmp signalling also characterize human salivary gland SCC and head and neck SCC in general. Our work defines mechanisms by which β-catenin signals remodel chromatin and control induction and maintenance of tumour propagating cells. Further, it supports new strategies for the therapy of solid tumours.