Summary: This paper, which is the natural continuation of part I [S. Federico, B. Goldys, and F. Gozzi, SIAM J. Control Optim., 48, p. 4910-4937, (2010; Zbl 1208.49048)], studies a class of optimal control problems with state constraints where the state equation is a differential equation with delays. In part I, the problem is embedded in a suitable Hilbert space \(H\) and the regularity of the associated Hamilton-Jacobi-Bellman equation is studied. The goal of the present paper is to exploit the regularity result of part I to prove a verification theorem and find optimal feedback controls for the problem. While it is easy to define a feedback control formally following the classical case, the proof of its existence and optimality is hard due to lack of full regularity of \(V\) and to the infinite dimensionality of the problem. The theory developed is applied to study economic problems of optimal growth for nonlinear time-to-build models. In particular, we show the existence and uniqueness of optimal controls and their characterization as feedbacks.