This paper presents the extension of our previous investigation of confined round jets with large Reynolds numbers and large expansion ratios (Revuelta, Sánchez & Liñán 2002a) to the case of swirling jets with swirl numbers of order unity. In the absence of vortex breakdown, we encounter the four-region asymptotic structure identified earlier for the non-swirling jet, including a region of jet development where the azimuthal and axial velocity components are comparable. For the flow in the long recirculating eddy that forms downstream, where the pressure differences associated with the azimuthal motion become negligible, the jet is found to act as a point source with momentum flux equal to the flow force of the incoming jet, and angular momentum flux equal to that of the jet at the orifice. The solution for the weak circulation in this slender region, including the parameter-free leading-order description and the first-order corrections, is determined by integrating the azimuthal component of the momentum equation written in the boundary-layer approximation. The results are validated through comparisons with numerical integrations of the steady axisymmetric Navier–Stokes equations, which are also used to evaluate critical conditions for vortex breakdown.