This letter reports on high extraction efficiency light-emitting diodes (LEDs) based on embedded two-dimensional air-gap photonic crystals (PhCs). High refractive index contrast provided by the air gaps along with high interaction of the embedded PhCs with the guided light resulted in an efficient extraction of all guided modes in the LED, in contrast to the common surface PhC configuration. Embedded PhC LEDs presented an enhanced directional light emission compared to non-PhC LEDs. High extraction efficiency, close to unity, provided by the encapsulated embedded PhC LEDs demonstrates the capability of this approach to achieve high efficiency devices with directional light emission.