This paper considers the problem of variable-length intrinsic randomness. We propose the average variational distance as the performance criterion from the viewpoint of a dual relationship with the problem formulation of variable-length resolvability. Previous study has derived the general formula of the $ε$-variable-length resolvability. We derive the general formula of the $ε$-variable-length intrinsic randomness. Namely, we characterize the supremum of the mean length under the constraint that the value of the average variational distance is smaller than or equal to a constant $ε$. Our result clarifies a dual relationship between the general formula of $ε$-variable-length resolvability and that of $ε$-variable-length intrinsic randomness. We also derive a lower bound of the quantity characterizing our general formula.