Because of the premature debonding of fiber-reinforced polymer (FRP) materials that results in a reduction in ductility, the problem of how to exploit moment redistribution (MR) in FRP-strengthened continuous reinforced concrete (RC) structures is unresolved. To date, limited research has been conducted into MR in such structures; a reliable and rigorous solution for quantifying MR throughout the loading cycle remains elusive. This paper aims to quantify MR and predict the capacity at reasonable accuracy, to encourage the use of FRP for the strengthening of existing continuous RC structures. Experiments conducted on 12 continuous T-beams are reported, and the findings are discussed. Strengthening configuration and anchorage scheme are the main variables. A new analytical strategy is described for quantifying MR, and the analytical results are then validated against the experimental results. Both experimental and analytical results confirm that there is no reason to restrict MR into strengthened zones. More importantly, MR, out of FRP-strengthened zones, can indeed occur, provided that the FRP is sufficiently anchored; reliable exploitation of this is now possible.