  Cu$_2$OSeO$_3$ is an insulating skyrmion-host material with a magnetoelectric
coupling giving rise to an electric polarization with a characteristic
dependence on the magnetic field $\vec H$. We report magnetic force microscopy
imaging of the helical real-space spin structure on the surface of a bulk
single crystal of Cu$_2$OSeO$_3$. In the presence of a magnetic field, the
helimagnetic order in general reorients and acquires a homogeneous component of
the magnetization, resulting in a conical arrangement at larger fields. We
investigate this reorientation process at a temperature of 10~K for fields
close to the crystallographic $\langle 110\rangle$ direction that involves a
phase transition at $H_{c1}$. Experimental evidence is presented for the
formation of magnetic domains in real space as well as for the microscopic
origin of relaxation events that accompany the reorientation process. In
addition, the electric polarization is measured by means of Kelvin-probe force
microscopy. We show that the characteristic field dependency of the electric
polarization originates in this helimagnetic reorientation process. Our
experimental results are well described by an effective Landau theory
previously invoked for MnSi, that captures the competition between
magnetocrystalline anisotropies and Zeeman energy.
