We theoretically study the lattice relaxation in the twisted bilayer graphene (TBG) and its effect on the electronic band structure. We develop an effective continuum theory to describe the lattice relaxation in general TBGs and obtain the optimized structure to minimize the total energy. At small rotation angles $< 2^{circ}$, in particular, we find that the relaxed lattice drastically reduces the area of AA-stacking region, and form a triangular domain structure with alternating AB and BA stacking regions. We then investigate the effect of the domain formation on the electronic band structure. The most notable change from the non-relaxed model is that an energy gap up to 20meV opens at the superlattice subband edges on the electron and hole sides. We also find that the lattice relaxation significantly enhances the Fermi velocity, which was strongly suppressed in the non-relaxed model.
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