Context. Swift J0243.6+6124 is a unique system. It is the first and only ultra-luminous X-ray source in our Galaxy. It is the first and only high-mass Be X-ray pulsar showing radio jet emission. It was discovered during a giant X-ray outburst in October 2017. While there are numerous studies in the X-ray band, very little is known about the optical counterpart. Aims. Our aim is to characterize the variability timescales in the optical and infrared bands in order to understand the nature of this intriguing system. Methods. We performed optical spectroscopic observations to determine the spectral type. Long-term photometric light curves together with the equivalent width of the Hα line were used to monitor the state of the circumstellar disk. We used BVRI photometry to estimate the interstellar absorption and distance to the source. Continuous photometric monitoring in the B and V bands allowed us to search for intra-night variability. Results. The optical counterpart to Swift J0243.6+6124 is a V = 12.9, O9.5Ve star, located at a distance of ∼5 kpc. The optical extinction in the direction of the source is AV = 3.6 mag. The rotational velocity of the O-type star is 210 km s-1. The long-term optical variability agrees with the growth and subsequent dissipation of the Be circumstellar disk after the giant X-ray outburst. The optical and X-ray luminosity are strongly correlated during the outburst, suggesting a common origin. We did not detect short-term periodic variability that could be associated with nonradial pulsations from the Be star photosphere. Conclusions. The long-term optical and infrared pattern of variability of Swift J0243.6+6124 is typical of Be/X-ray binaries. However, the absence of nonradial pulsations is unusual and adds another peculiar trait to this unique source. ; With funding from the Spanish government through the "María de Maeztu Unit of Excellence" accreditation (MDM-2017-0737)
