Brueckner orbitals are the optimal orbitals for use in F12 explicitly correlated coupled-cluster (CC) treatments. A novel approach, Brueckner coupled-cluster doubles with perturbative triples BCCD(T)(F12) is presented that avoids the expensive re-evaluation of F12 integrals throughout the orbital optimisation and includes a newly derived basis set correction to the Brueckner reference energy. The generalisation of F12 theory to arbitrary non-Hartree-Fock references and to Fock operators that include scalar relativistic effects is also presented. The performance of the new Brueckner F12 method is assessed for a test set of 50 open- and closed-shell reactions and for the ionisation potentials and electron affinities (EAs) of the first-row transition metal atoms. Benchmark basis set limit coupled-cluster singles, doubles and perturbative triples (CCSD(T)) and BCCD(T) values are reported for all energies in the test sets. BCCD(T)(F12) performs systematically better than CCSD(T)(F12) for electron affinities where orbital relaxation effects are significant.