Eight members of the R₂TeO₆ family for the neutron non-absorbing rare-earths (R = La, Pr, Nd, Tb, Ho, Er, Tm, Lu) have been synthesized by solid-state reactions as pure specimens and structurally characterized by neutron powder diffraction (NPD), allowing for the precise determination of the oxygen positions and thermal displacements in the presence of heavy rare-earth and tellurium atoms. For the large rare-earth cations (from La³⁺ to Tm³⁺) the crystal structure adopts the Nd₂WO₆ type, defined in the orthorhombic P2₁2₁2₁ space group, containing two types of crystallographically independent rare earth atoms, R1 and R2, sevenfold coordinated with oxygen atoms; the tellurium atoms form distorted TeO₆ octahedra, sharing corners and edges with both kinds of R1O₇ and R2O₇ polyhedra. For Lu₂TeO₆ a morphotropic phase transition is observed, and this compound crystallizes in the trigonal P321 space group, with two RO₆ and two independent TeO₆ coordination polyhedra, also sharing vertices. For Yb₂TeO₆ a mixture of orthorhombic and trigonal phases is identified. A bond valence study, confirming that R is trivalent and Te is hexavalent in the whole series, helps to understand the driving force for the morphotropic transition to a more stable crystal structure where Lu³⁺ adopts a lower coordination index.