It is shown that the world volume field theory of a single D3-brane in a su
pergravity D3-brane background admits finite energy, and non-singular, Abel
ian monopoles and dyons preserving 1/2 or 1/4 of the N=4 supersymmetry and
saturating a Bogomol' nyi-type bound. The 1/4 supersymmetric solitons provi
de a world volume realization of string-junction dyons. We also discuss the
dual M-theory realization of the 1/2 supersymmetric dyons as finite tensio
n self-dual strings on the M5-brane, and of the 1/4 supersymmetric dyons as
their intersections. [S0556-2821(99)04116-8].