Colloidal quantum dots (QDs) have emerged as promising color conversion light emitters for solid-state lighting applications [Nat. Photonics 7, 13 (2012) due to their emission tunability and near-unity photoluminescence quantum yields. In the current commercial LEDs, QDs are dispersed into an encapsulation layer in a far-field architecture, where the majority of the light emitted by the LED remains trapped within the epitaxy due to total internal reflection, drastically reducing the out-coupling efficiency. In this paper, we demonstrate a photonic quasi-crystal hybrid LED geometry that allows QD emitters to be placed in close proximity to the multiple quantum wells (MQWs) of the active area. This architecture greatly improves the coupling between MQWs and QDs, simultaneously allowing for a nonradiative resonant energy transfer between the MQWs and the QDs and near-field radiative coupling of trapped (guided) modes in the LED to the emitters. In this configuration, we demonstrate record-breaking effective quantum yields reaching 123% for single-color conversion LEDs and 110% for white light-emitting devices.