Low-temperature measurements of the magnetocrystalline anisotropy energy \(K\) in (Fe\(_{1-x}\)Co\(_{x}\))\(_{2}\)B alloys are reported, and the origin of this anisotropy is elucidated using a first-principles electronic structure analysis. The calculated concentration dependence \(K(x)\) with a maximum near \(x=0.3\) and a minimum near \(x=0.8\) is in excellent agreement with experiment. This dependence is traced down to spin-orbital selection rules and the filling of electronic bands with increasing electronic concentration. At the optimal Co concentration, \(K\) depends strongly on the tetragonality and doubles under a modest 3% increase of the \(c/a\) ratio, suggesting that the magnetocrystalline anisotropy can be further enhanced using epitaxial or chemical strain.