The magnetic and electronic properties of transition metal borates Me3B2O6 (Me = Mn, Fe, Co, Ni) with kotoite structure have been investigated at ambient and high pressures via a combination of representation analysis and density functional theory (DFT + U) calculations. Several magnetic configurations corresponding to the different irreducible representations have been considered. The total-energy calculations reveal that the magnetic ground state of Me3B2O6 kotoites is composition-dependent. The lowest energy magnetic phase of manganese and nickel kotoites is characterized by the antiferromagnetic ordering of the transition metal magnetic moments along the c- axis and along the b-axis for cobalt and iron kotoites. The magnetic cell of Ni3B2O6 kotoite corresponds to k = (1/2, 0, 1/2) vector and four time larger than the unit cell. The calculated exchange constants indicate the competition between ferromagnetic and antiferromagnetic interactions. At a critical pressure, Me ions undergo a high-spin to low-spin state crossover. This magnetic moments collapse is analyzed in terms of change in electronic structure under pressure.