We present clear evidence of the formation of three-dimensional (3D) plasmoids in the current sheet between two magnetic flux systems in a 3D numerical experiment of flux emergence into the solar atmosphere and study their properties and time evolution. Plasmoids are most likely the result of resistive tearing mode instabilities. They adopt the shape of a solenoid contained within the current sheet: the solenoid is tightly wound when the field in the two flux systems is close to antiparallel. The plasmoids are expelled to the sides of the sheet as a result of a reconnection imbalance between the two x-lines on their sides. We show the complex, 3D field line geometry in various plasmoids: individual plasmoid field lines have external linkages to the flux system on either side of the current sheet; we also find field lines that go through a few plasmoids in succession, probably indicating that the field line has resulted from multiple reconnection events.