In this paper JK_s-band data from the VISTA Magellanic Cloud (VMC) survey are used to investigate the tip of the red giant branch (TRGB) as a distance indicator. A linear fit to recent theoretical models is used as the basis for the absolute calibration which reads M_Ks = −4.196 − 2.013 (J − K_s), valid in the colour range 0.75 < (J − K_s)< 1.3 mag and in the 2MASS system. The observed TRGB is found based on a classical first-order derivative filter and a second-order derivative filter applied to the binned luminosity function using the “sharpened” magnitude that takes the colour term into account. Extensive simulations are carried out to investigate any biases and errors in the derived distance modulus (DM). Based on these simulations criteria are established related to the number of stars per bin in the 0.5 mag range below the TRGB and related to the significance with which the peak in the filter response curve is determined such that the derived distances are unbiased. The DMs based on the second-order derivative filter are found to be more stable and are therefore adopted, although this requires twice as many stars per bin. Given the surface density of TRGB stars in the Magellanic Clouds (MCs), areas of ∼0.5 deg² in the densest parts to ∼10 deg² in the outskirts of the MCs need to be considered to obtain accurate and reliable values for the DMs. The TRGB method is applied to specific lines-of-sight where independent distance estimates exist, based on detached eclipsing binaries in the Large and Small Magellanic Clouds (LMC, SMC), classical Cepheids in the LMC, RR Lyrae stars in the SMC, and fields in the SMC where the star formation history (together with reddening and distance) has been derived from deep VMC data. The analysis shows that the theoretical calibration is consistent with the data, that the systematic error on the DM is approximately 0.045 mag (about evenly split between the theoretical calibration and the method), and that random errors of 0.015 mag are achievable. Reddening is an important element in deriving the distance: we derive mean DMs ranging from 18.92 mag (for a typical E(B − V) of 0.15 mag) to 19.07 mag (E(B − V)∼0.04 mag) for the SMC, and ranging from 18.48 mag (E(B − V)∼0.12 mag) to 18.57 mag (E(B − V)∼0.05 mag) for the LMC.