We present a family of three-dimensional nonlinear solutions for magnetic field annihilation in a current sheet, including the effects of resistivity and viscosity. The different members of the family are characterized by the imposed vorticity of the flow that brings the field lines together. Since in a three-dimensional flow the vorticity can be increased by the stretching of vortex lines (an effect that is absent in two dimensions), we find some striking differences to our previous two-dimensional analysis. In both the two-dimensional and three-dimensional analyses, above a certain critical imposed vorticity &ohgr;crit, the flow breaks up into cells with current sheets at their boundaries. The nature of the original central current sheet is completely altered. In the two-dimensional analysis, &ohgr;crit is a steeply increasing function of the viscous Reynolds number R, whereas in the three-dimensional case, it quickly asymptotes to only &ohgr;crit=2v0/L where v0 and L are the characteristic velocity and length scale of the flow, respectively. The width of the current sheet, which depends on the speed at which field lines are carried into it, also responds differently to an increase in R. In two dimensions, the current sheet narrows for all vorticities, but in three dimensions, it narrows when the imposed vorticity is negative and widens when it is positive. Also we find that the current density within the current sheet varies as the nature of the flow is changed, rather than being constant as in the two-dimensional case. Finally, we find that there is a minimum value of the plasma beta &bgr;min below which the plasma pressure is negative. For the nonsheared (neutral current sheet) case, &bgr;min increases rapidly with the magnetic Reynolds number Rm such that this type of annihilation is only possible for a high-beta plasma. For a sheared magnetic field, however, &bgr;min is much lower, making this type of annihilation more relevant to the solar corona. ¿ American Geophysical Union 1993