We present magnetodielectric measurements in single crystals of the cubic spin-1/2 compound Cu2OSeO3. A magnetic-field-induced electric polarization (P) and a finite magnetocapacitance (MC) is observed at the onset of the magnetically ordered state (T-c = 59 K). Both P and MC are explored in considerable detail as a function of temperature (T), applied field H-a, and relative field orientations with respect to the crystallographic axes. The magnetodielectric data show a number of anomalies which signal magnetic phase transitions, and allow us to map out the phase diagram of the system in the H-a-T plane. Below the 3-up-1-down collinear ferrimagnetic phase, we find two additional magnetic phases. We demonstrate that these are related to the field-driven evolution of a long-period helical phase, which is stabilized by the chiral Dzyaloshinskii-Moriya term DM . ((V) over bar x M) that is present in this noncentrosymmetric compound. We also present a phenomenological Landau-Ginzburg theory for the magnetic-field-induced electric polarization (MEH) effect, which is in excellent agreement with experimental data, and shows three main features: (i) the polarization P has a uniform as well as a long-wavelength spatial component that is given by the pitch of the magnetic helices, (ii) the uniform component of P points along the vector (HyHz,H-z H-x,H-x H-y),and (iii) its strength is proportional to eta(2)(parallel to) - eta(2)(perpendicular to)/2, where eta(parallel to) is the longitudinal and eta(perpendicular to) is the transverse (and spiraling) component of the magnetic ordering. Hence, the field dependence of P provides a clear signature of the evolution of a conical helix under a magnetic field. A similar phenomenological theory is discussed for the MC.