We present the results of the first neutron powder and single crystal diffraction studies of the coupled spin tetrahedra systems Cu2Te2O5X2 (X = Cl,Br). Incommensurate antiferromagnetic order with the propagation vectors kCl approximately [0.150,0.422,1/2], kBr approximately [0.158,0.354,1/2] sets in below TN = 18 K for X = Cl and 11 K for X = Br. No simple collinear antiferromagnetic or ferromagnetic spin arrangements within Cu2+ tetrahedra fit these observations. Fitting the diffraction data to more complex but physically reasonable models with multiple helices leads to a moment of 0.67(1)microB/Cu2+ at 1.5 K for the Cl compound. The reason for such a complex ground state may be geometrical frustration of the spins due to the intratetrahedral and intertetrahedral couplings having similar strengths. In neither compound has any evidence for a structural transition accompanying the magnetic ordering been found.