In the present work, we report the outstanding magneto-elastic and magneto-caloric properties of a Tb-Co binary amorphous alloy. The glass forming ability (GFA) of Tb-Co binary alloys was studied and the best glass former was obtained near the eutectic point of the binary alloys. The magnetic properties of the eutectic Tb62.5Co37.5 amorphous alloy were measured, and it was found that the Tb62.5Co37.5 amorphous ribbons exhibited excellent magneto-elastic properties (the magnetostriction of nearly 470 ppm at 50 K under 5 T) and magneto-caloric properties (the peak magnetic entropy change of 9.3 Jkg−1K−1 at 92.5 K under 5 T). The mechanism for the improved GFA, magneto-caloric effect (MCE) and magneto-elastic properties of the Tb62.5Co37.5 amorphous ribbons was analyzed. Display omitted •The Tb62.5Co37.5 amorphous alloy is found to be the best glass former in the Tb-Co binary alloys.•The alloy exhibits excellent magnetocaloric effect and magnetoelastic properties.•The high -ΔSmpeak value of the Tb62.5Co37.5 amorphous alloy is related to its high compositional moment.•The rigid rotation of the clusters in the amorphous alloy leads to its high magnetostriction.