Triple-junction solar cells from III-V compound semiconductors have thus far delivered the highest solar-electric conversion efficiencies. Increasing the number of junctions generally offers the potential to reach even higher efficiencies, but material quality and the choice of bandgap energies turn out to be even more importance than the number of junctions. Several four-junction solar cell architectures with optimum bandgap combination are found for lattice-mismatched III-V semiconductors as high bandgap materials predominantly possess smaller lattice constant than low bandgap materials. Direct wafer bonding offers a new opportunity to combine such mismatched materials through a permanent, electrically conductive and optically transparent interface. In this work, a GaAs-based top tandem solar cell structure was bonded to an InP-based bottom tandem cell with a difference in lattice constant of 3.7%. The result is a GaInP/GaAs//GaInAsP/GaInAs four-junction solar cell with a new record efficiency of 44.7% at 297-times concentration of the AM1.5d (ASTM G173-03) spectrum. This work demonstrates a successful pathway for reaching highest conversion efficiencies with III-V multi-junction solar cells having four and in the future even more junctions.