The eROSITA X-ray telescope onboard the Spectrum-Roentgen-Gamma (SRG) observatory combines a large field of view and a large collecting area in the energy range between ~0.2 and ~8.0 keV with the capability to perform uniform scanning observations of large sky areas. SRG/eROSITA performed scanning observations of the ~140 square degrees eROSITA Final Equatorial Depth Survey field (the eFEDS field) as part of its performance verification phase ahead of the planned four years of all-sky scanning operations. The observing time of eFEDS was chosen to slightly exceed the depth expected in an equatorial field after the completion of the all-sky survey. While verifying the capability of eROSITA to perform large area uniform surveys and serving as a test and training dataset to establish calibration and data analysis procedures, the eFEDS survey also constitutes the largest contiguous soft X-ray survey at this depth to date, supporting a range of early eROSITA survey science investigations. Here we present a catalogue of detected X-ray sources in the eFEDS field providing source positions and extent information, as well as fluxes in multiple energy bands. The data were fed through a standard data processing pipeline, which applies X-ray event calibration and provides a set of standard calibrated data products. A multi-stage source detection procedure, building in part on experience from XMM-Newton, was optimized and calibrated by performing realistic simulations of the eROSITA eFEDS observations. Source fluxes are computed in multiple standard energy bands, both by forced PSF-fitting and aperture photometry. We cross-matched the eROSITA eFEDS source catalogue with previous XMM-ATLAS observations, confirming excellent agreement of the eROSITA and XMM-ATLAS source fluxes. Astrometric corrections were performed by cross-matching the eROSITA source positions with an optical reference catalogue of quasars. We present a primary catalogue of 27910 X-ray sources (including 542 with significant spatial extent) detected in the 0.2-2.3keV energy range with detection likelihoods >6, corresponding to a (point source) flux limit of 6.5*10^-15^erg/cm^2^/s in the 0.5-2.0keV energy band (80% completeness). A supplementary catalogue contains 4774 low-significance source candidates with detection likelihoods between 5 and 6. In addition, a hard band sample of 246 sources detected in the energy range 2.3-5.0keV above a detection likelihood of 10 is provided. Finally, we provide in appendix a description of the dedicated data analysis software package, of the eROSITA calibration database and of the standard calibrated data products.