Gather all ingredients.

Combine sugar, cornstarch, cocoa powder, and milk in a small saucepan over medium heat. Bring to a simmer and stir until thick, about 2 minutes. Remove from heat; stir in vanilla and butter.

Transfer to a heatproof bowl and refrigerate until cool, approximately 20 minutes.

Stir chocolate chips into the cooled chocolate mixture.

Pour into your favorite popsicle molds and freeze until solid, about 4 hours.

To serve, run warm water over the molds until fudge pops slide out easily.