In this work, we explore the statistical copolymerization of 1,3-butadiene with the terpenic monomers myrcene and farnesene, carried out via coordination polymerization using a neodymium-based ternary catalytic system. The resultant copolymers, poly(butadiene-co-myrcene) and poly(butadiene-co-farnesene), were synthesized at different monomer ratios, elucidating the influence of the bio-based monomer content over the kinetic variables, molecular and thermal properties, and the reactivity constants (Fineman-Ross and Kelen-Tudos methods) of the resultant copolymers. The results indicate that through the herein employed conditions, it is possible to obtain more sustainable high-cis (approximate to 95%) polybutadiene elastomers with random and tunable content of bio-based monomer. Moreover, the polymers exhibit fairly high molecular weights and a rather low dispersity index. Upon copolymerization, the T-g of high-cis PB can be shifted from -106 to -75 degrees C (farnesene) or -107 to -64 degrees C (myrcene), without altering the microstructure control. This work contributes to the development of more environmentally friendly elastomers, to form green rubber materials.