Polycrystalline samples and single crystals of four members of the new complex boride series Ti3-xRu5-yIryB2+x (0 <= x <= 1 and 1 < y < 3) were synthesized by arc-melting the elements in a water-cooled copper crucible under an argon atmosphere. The new silvery phases were structurally characterized by powder and single-crystal X-ray diffraction as well as energy- and wavelength-dispersive X-ray spectroscopy analyses. They crystallize with the tetragonal Ti3Co5B2 structure type in space group P4/mbm (No. 127). Tetragonal prisms of Ru/Ir atoms are filled with titanium in the boron-poorest phase (Ti3Ru2.9Ir2.1B2). Gradual substitution of titanium by boron then results in the successive filling of this site by a Ti/B mixture en route to the complete boron occupation, leading to the boron-richest phase (Ti2Ru2.8Ir2.2B3). Furthermore, both ruthenium and iridium share two sites in these structures, but a clear Ru/Ir site preference is found. First-principles density functional theory calculations (Vienna ab kith() simulation package) on appropriate structural models (using a supercell approach) have provided more evidence on the stability of the boron-richest and -poorest phases, and the calculated lattice parameters corroborate very well with the experimentally found ones. Linear muffin-tin orbital atomic sphere approximation calculations further supported these findings through crystal orbital Hamilton population bonding analyses, which also show that the Ru/Ir-B and Ru/Ir-Ti heteroatomic interactions are mainly responsible for the structural stability of these compounds. Furthermore, some stable and unstable phases of this complex series could be predicted using the rigid-band model. According to the density of states analyses, all phases should be metallic conductors, as was expected from these metal-rich borides.