[Abbreviated] The amount of integral field spectrograph (IFS) data has grown considerable over the last few decades. The demand for tools to analyze such data is therefore bigger now than ever. We present TDOSE; a flexible Python tool for Three Dimensional Optimal Spectral Extraction from IFS data cubes. TDOSE works on any three-dimensional data cube and bases the spectral extractions on morphological reference image models. In each wavelength layer of the IFS data cube, TDOSE simultaneously optimizes all sources in the morphological model to minimize the difference between the scaled model components and the IFS data. The flux optimization produces individual data cubes containing the scaled three-dimensional source models. This allows for efficient de-blending of flux in both the spatial and spectral dimensions of the IFS data cubes, and extraction of the corresponding one-dimensional spectra. We present an example of how the three-dimensional source models generated by TDOSE can be used to improve two-dimensional maps of physical parameters. By extracting TDOSE spectra of $sim$150 [OII] emitters from the MUSE-Wide survey we show that the median increase in line flux is $sim$5% when using multi-component models as opposed to single-component models. However, the increase in recovered line emission in individual cases can be as much as 50%. Comparing the TDOSE model-based extractions of the MUSE-Wide [OII] emitters with aperture spectra, the TDOSE spectra provides a median flux (S/N) increase of 9% (14%). Hence, TDOSE spectra optimizes the S/N while still being able to recover the total emitted flux. TDOSE version 3.0 presented in this paper is available at https://github.com/kasperschmidt/TDOSE.
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