Aims. HR2562 is an F5V star located at similar to 33 pc from the Sun hosting a substellar companion that was discovered using the Gemini planet imager (GPI) instrument. The main objective of the present paper is to provide an extensive characterization of the substellar companion, by deriving its fundamental properties. Methods. We observed HR2562 with the near-infrared branch composed by the integral field spectrograph (IFS) and the infrared dual band spectrograph (IRDIS) of the spectro-polarimetric high-contrast exoplanet research (SPHERE) instrument at the very large telescope (VLT). During our observations IFS was operating in the YJ band, while IRDIS was observing with the H broadband filter. The data were reduced with the dedicated SPHERE GTO pipeline, which is custom designed for this instrument. On the reduced images, we then applied the post-processing procedures that are specifically prepared to subtract the speckle noise. Results. The companion is clearly detected in both IRDIS and IFS datasets. We obtained photometry in three different spectral bands. The comparison with template spectra allowed us to derive a spectral type of T2-T3 for the companion. Using both evolutionary and atmospheric models we inferred the main physical parameters of the companion obtaining a mass of 32 +/- 14 M-Jup, T-eff = 1100 +/- 200 K, and log g = 4.75 +/- 0.41.