Aims. With the purpose of producing the first detailed full view of Puppis A in X-rays, we carried out new XMM-Newton observations covering the missing regions in the southern half of the supernova remnant (SNR) and combined them with existing XMM-Newton and Chandra data. Methods. Two pointings toward the south and southwest of Puppis A were observed with XMM-Newton. We combined these data with archival XMM-Newton and Chandra data and produced images in the 0.3−0.7, 0.7−1.0, and 1.0−8.0 energy bands. Results. We present the first sensitive complete X-ray image of Puppis A. We investigated its morphology in detail, carried out a multiwavelength analysis, and estimated the flux density and luminosity of the whole SNR. The complex structure observed across the remnant confirms that Puppis A evolves in an inhomogeneous, probably knotty interstellar medium. The southwestern corner includes filaments that perfectly correlate with radio features suggested to be associated with shock/cloud interaction. In the northern half of Puppis A the comparison with Spitzer infrared images shows an excellent correspondence between X-rays and 24 and 70 μm emission features, while to the south there are some matched and other unmatched features. X-ray flux densities of 12.6 × 10 −9 , 6.2 × 10 −9 , and 2.8 × 10 −9 erg cm −2 s −1 were derived for the 0.3−0.7, 0.7−1.0, and 1.0−8.0 keV bands, respectively. At the assumed distance of 2.2 kpc, the total X-ray luminosity between 0.3 and 8.0 keV is 1.2 ×10 37 erg s −1 . We also collected and updated the broad-band data of Puppis A between radio and GeV γ-ray range, producing its spectral energy distribution. To provide constraints to the high-energy emission models, we re-analyzed radio data, estimating the energy content in accelerated particles to be U min = 4.8 × 10 49 erg and the magnetic field strength B ∼ 26 μG.