Nanocrystalline Lu3Ga5O12 garnets doped with Tm(3+)/Yb(3+) ions have been synthesized by a low cost and environmentally benign sol-gel technique and characterized for their structural, Stokes and anti-Stokes luminescence properties. The diffuse reflectance spectra of doped Lu3Ga5O12 nano-garnets have been measured to derive the partial energy level structure of Tm(3+) and Yb(3+) ions and possible energy transfer channels between them. Upon laser excitation at 473 nm, weak red and intense near-infrared Stokes emissions have been observed in the nano-garnets. The decay curves of (3)H4 and (1)G4 levels of Tm(3+) ions and the (2)F5/2 level of Yb(3+) ions have been measured upon resonant laser excitation and are found to be non-exponential in nature due to multipolar interactions. In order to know the kind of multipolar interaction among optically active ions, the decay curves are analyzed through the generalized Yokota-Tanimoto model. Moreover, under 970 nm laser excitation, intense blue anti-Stokes emission is observed by the naked eye in Tm(3+)-Yb(3+) co-doped Lu3Ga5O12 nano-garnets. The results show that as-synthesized nano-garnets may be useful in the field of phosphors and photonics.