We present a fast model-based inversion algorithm for quantitative 2-D and 3-D optoacoustic tomography. The algorithm is based on an accurate and efficient forward model, which eliminates the need for regularization in the inversion process while providing modeling flexibility essential for quantitative image formation. The resulting image-reconstruction method eliminates stability problems encountered in previously published model-based techniques and, thus, enables performing image reconstruction in real time. Our model-based framework offers a generalization of the forward solution to more comprehensive optoacoustic propagation models, such as including detector frequency response, without changing the inversion procedure. The reconstruction speed and other algorithmic performances are demonstrated using numerical simulation studies and experimentally on tissue-mimicking optically heterogeneous phantoms and small animals. In the experimental examples, the model-based reconstructions manifested correctly the effect of light attenuation through the objects and did not suffer from the artifacts which usually afflict the commonly used filtered backprojection algorithms, such as negative absorption values.