By a quiver setting we mean a pair \((Q,\alpha)\) consisting of a quiver \(Q\) and a dimension vector \(\alpha\). Given a quiver setting \((Q,\alpha)\) one defines the representation space \(\text{Rep}(Q,\alpha)\) which carries a natural action of the group \(\text{GL}_\alpha\), which is the product of the general linear groups corresponding to the vertices of the quiver \(Q\). The setting \((Q,\alpha)\) is called cofree if the coordinate ring \(\mathbb{C}[\text{Rep}(Q,\alpha)]\) is a graded free module over the ring \(\mathbb{C}[\text{Rep}(Q,\alpha)]^{\text{GL}_\alpha}\) of invariants. In the paper, the authors classify the cofree quiver setting in terms of their prime strongly connected components and a (so called) wedging operation. The main tool used in the proof is a theorem of \textit{V. L. Popov} [Funct. Anal. Appl. 10, 242-244 (1976); translation from Funkts. Anal. Prilozh. 10, No. 3, 91-92 (1976; Zbl 0365.20053)], which (in the considered context) states that a quiver setting \((Q,\alpha)\) is cofree if and only if it is coregular (i.e.\ \(\mathbb{C}[\text{Rep}(Q,\alpha)]^{\text{GL}_\alpha}\) is a polynomial ring) and the codimension in \(\text{Rep}(Q,\alpha)\) of the nullcone (i.e.\ the zero set of the invariants of positive degree) equals the Krull dimension of \(\mathbb{C}[\text{Rep}(Q,\alpha)]^{\text{GL}_\alpha}\). Then the authors use a classification of coregular quiver settings obtained by the first author [J. Algebra 253, No. 2, 296-313 (2002; Zbl 1041.16010)] and properties of the nullcone obtained by the second author [J. Algebra 274, No. 1, 373-386 (2004; Zbl 1078.14066)].