Optoacoustic tomography is a fast developing imaging modality, combining the high contrast available from optical excitation of tissue with the high resolution and penetration depth of ultrasound detection. Light is subject to both absorption and scattering when traveling through tissue; adequate knowledge of tissue optical properties and hence the spatial fluence distribution is required to create an optoacoustic image that is directly proportional to chromophore concentrations at all depths. Using data from a commercial multispectral optoacoustic tomography (MSOT) system, we implemented an iterative optimization for fluence correction based on a finite-element implementation of the delta-Eddington approximation to the Radiative Transfer Equation (RTE). We demonstrate a linear relationship between the image intensity and absorption coefficients across multiple wavelengths and depths in phantoms. We also demonstrate improved feature visibility and spectral recovery at depth in phantoms and with in vivo measurements, suggesting our approach could in the future enable quantitative extraction of tissue absorption coefficients in biological tissue.