High Energy Research Organization (KEK) has engaged in development of the beam separation dipole, MBXF, toward the HL-LHC project. The magnet has a full length of 7 m and generates a magnetic field of 5.6 T in the magnet center at nominal operating condition of 12 kA and 1.9 K. Optimization of the magnetic model is performed through two and three dimensional studies and iterated until resultant field quality is within required tolerance. Field quality of the first full-scale prototype of MBXF (a.k.a. MBXFP1) is measured first at room temperature on the premises of the manufacturer, Hitachi Ltd. This result is used for comparison with the numerical models and the first validation of our design methodology. After then a further model tuning is considered for the magnetic design of the first series. The final validation of our design methodology is performed after the cold test of MBXFP1 in the vertical cryostat in KEK facilities. Finally we determine a magnetic design of the first series production with an expected sextupole integral and decapole integral, which are major systematic contributions to the field quality of MBXF, estimated to be $0.0 \pm 1.6$ units and $1.1 \pm 0.2$ units, respectively.