International audienceWe derive galaxy colour selections from Euclid and ground-based photometry, aiming to accurately define background galaxy samples in cluster weak-lensing analyses. These selections are implemented in the Euclid data analysis pipelines for galaxy clusters. Given any set of photometric bands, we develop a method for the calibration of optimal galaxy colour selections that maximises the selection completeness, given a threshold on purity. Such colour selections are expressed as a function of the lens redshift. We calibrate galaxy selections using ground-based griz and Euclid YEJEHE bands. Both selections produce a purity higher than 97%. The griz selection completeness ranges from 30% to 84% in the lens redshift range zl∈[0.2,0.8]. With the full grizYEJEHE selection, the completeness improves by up to 25 percentage points, and the zl range extends up to zl=1.5. The calibrated colour selections are stable to changes in the sample limiting magnitudes and redshift, and the selection based on griz bands provides excellent results on real and simulated external data sets. Furthermore, the calibrated selections provide stable results using alternative photometric aperture definitions obtained from different ground-based telescopes. The griz selection is also purer at high redshift and more complete at low redshift compared to colour selections found in the literature. We show that the calibrated colour selections provide robust results even when observations from a single band are missing from the ground-based data. Finally, we show that colour selections imply variations within the 1σ uncertainty in the mean multiplicative shear bias, m, for stage III surveys. The first Euclid data releases will provide further insights into the impact of background selections on m