The incorporation and site preference of minor amounts (about 1 wt%) of Yb3+ in synthetic pyrope (Mg3Al2Si3O12) and grossular (Ca3Al2Si3O12) garnet were studied by X-ray Absorption Fine-Structure (XAFS) Spectroscopy. The measurements, performed in the temperature range 77-343 K at both Yb L-I- and L-III-edges, demonstrate that Yb3+ enters the garnet structure and is located in the dodecahedral site in both samples. The coordination environment of Yb3+ in the two samples was compared to that of the X-site cation in end-member synthetic pyrope and grossular and in Yb3Al5O12 as determined by single-crystal X-ray diffraction. The local geometry around Yb3+ is different from that of Mg and Ca in the bulk of the garnet, and also from that of Yb3+ in Yb3Al5O12. The XAFS results indicate that, (1) structural relaxation occurs around Yb3+ in the garnet structure; (2) the host garnet matrix exerts a major structural control on the incorporation of Yb3+ and (3) minor amounts of Yb3+ in garnet are located in structural sites and not in ill-defined defects.