We present a comprehensive study of the electroweak phase transition in composite Higgs models, where the Higgs arises from a new, strongly-coupled sector which confines near the TeV scale. This work extends our study in ref. {[}1]. We describe the confinement phase transition in terms of the dilaton, the pseudo-Nambu-Goldstone boson of broken conformal invariance of the composite Higgs sector. From the analysis of the joint Higgs-dilaton potential we conclude that in this scenario the electroweak phase transition can naturally be first-order, allowing for electroweak baryogenesis. We then extensively discuss possible options to generate a sufficient amount of CP violation another key ingredient of baryogenesis from quark Yukawa couplings which vary during the phase transition. For one such an option, with a varying charm quark Yukawa coupling, we perform a full numerical analysis of tunnelling in the Higgs-dilaton potential and determine regions of parameter space which allow for successful baryogenesis. This scenario singles out the light dilaton region while satisfying all experimental bounds. We discuss future tests. Our results bring new opportunities and strong motivations for electroweak baryogenesis.