Accurately accounting for the AGN phase in galaxy evolution requires a large, clean AGN sample. This is now possible with SRG/eROSITA, which completed its first all-sky X-ray survey (eRASS1) on June 12, 2020. The public Data Release 1 (DR1, Jan 31, 2024) includes 930,203 sources from the Western Galactic Hemisphere. The data enable the selection of a large AGN sample and the discovery of rare sources. However, scientific return depends on accurate characterisation of the X-ray emitters, requiring high-quality multiwavelength data. This paper presents the identification and classification of optical and infrared counterparts to eRASS1 sources. Counterparts to eRASS1 X-ray point sources were identified using Gaia DR3, CatWISE2020, and Legacy Survey DR10 (LS10) with the Bayesian NWAY algorithm and trained priors. Sources were classified as Galactic or extragalactic via a Machine Learning model combining optical/IR and X-ray properties, trained on a reference sample. For extragalactic LS10 sources, photometric redshifts were computed using Circlez. Within the LS10 footprint, all 656,614 eROSITA/DR1 sources have at least one possible optical counterpart; ~570,000 are extragalactic and likely AGN. Half are new detections compared to AllWISE, Gaia, and Quaia AGN catalogues. Gaia and CatWISE2020 counterparts are less reliable, due to the survey's shallowness and the limited amount of features available to assess the probability of being an X-ray emitter. In the Galactic Plane, where the overdensity of stellar sources also increases the chance of associations, using conservative reliability cuts, we identify approximately 18000 Gaia and 55000 CatWISE2020 extragalactic sources. We release three high-quality counterpart catalogues - plus the training and validation sets - as a benchmark for the field. These datasets have many applications, but in particular empower researchers to build AGN samples tailored for completeness and purity, accelerating the hunt for the Universe's most energetic engines.

Cone search capability for table J/A+A/704/A344/dr1ls10 (Identification and characterization of the counterparts to the X-ray point sources in the eROSITA/DR1 main catalogue using the Legacy Survey DR10)

Cone search capability for table J/A+A/704/A344/dr1ge3 (Identification and characterization of the counterparts to the X-ray point sources in the eROSITA/DR1 main catalogue using the Gaia DR3 survey)

Cone search capability for table J/A+A/704/A344/dr1cw2020 (Identification and characterization of the counterparts to the X-ray point sources in the eROSITA/DR1 main catalogue using the CatWISE2020 survey)

Cone search capability for table J/A+A/704/A344/csc2ls10 (Legacy Survey DR10 counterparts to Chandra CSC2 and field population used for training)

Cone search capability for table J/A+A/704/A344/4xmmls10 (Legacy Survey DR10 counterparts to 4XMM and field population used for training)

Cone search capability for table J/A+A/704/A344/csc2ge3 (Gaia EDR3 counterparts to Chandra CSC2 and field population used for training)

Cone search capability for table J/A+A/704/A344/4xmmge3 (Gaia EDR3 counterparts to 4XMM and field population used for training)

Cone search capability for table J/A+A/704/A344/csc2wise (CatWISE2020 counterparts to Chandra CSC2 and field population used for training)

Cone search capability for table J/A+A/704/A344/4xmmcw20 (CatWISE2020 counterparts to 4XMM and field population used for training)