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Ionization injection triggered by short wavelength laser pulses inside a nonlinear wakefield driven by a longer wavelength laser is examined via multidimensional particle-in-cell simulations. We find that very bright electron beams can be generated through this two-color scheme in either collinear propagating or transverse colliding geometry. For a fixed laser intensity I, lasers with longer/shorter wavelength λ have larger/smaller ponderomotive potential (∝Iλ^{2}). The two-color scheme utilizes this property to separate the injection process from the wakefield excitation process. Very strong wakes can be generated at relatively low laser intensities by using a longer wavelength laser driver (e.g., a 10  μm CO_{2} laser) due to its very large ponderomotive potential. On the other hand, a short wavelength laser can produce electrons with very small residual momenta (p_{⊥}∼a_{0}∼sqrt[I]λ) inside the wake, leading to electron beams with very small normalized emittances (tens of nm). Using particle-in-cell simulations we show that a ∼10  fs electron beam with ∼4  pC of charge and a normalized emittance of ∼50  nm can be generated by combining a 10  μm driving laser with a 400 nm injection laser, which is an improvement of more than 1 order of magnitude compared to the typical results obtained when a single wavelength laser is used for both the wake formation and ionization injection. With the transverse colliding geometry, simulations show that similarly low emittance and much lower slice energy spread (∼30  keV, comparing with the typical value of few MeV in the longitudinal injection scheme) can be simultaneously obtained for electron beams with a few pC charge. Such low slice energy spread may have significant advantages in applications relevant to future coherent light sources driven by plasma accelerators.