We investigate the onset of driven collisionless reconnection and plasmoid formation in a magnetically dominated pair plasma, using 2D particle-in-cell simulations. Two force-free flux tubes of radius R are initially pushed together with a prescribed velocity, forming a current sheet whose width shrinks until reconnection sets in. Even in our largest simulation with R ≈ 1600 plasma skin depths, the sheet thickness at reconnection onset is comparable to the skin depth. Plasmoid chains develop when the sheet length-to-width aspect ratio A ≳ 30. In the strongly magnetized limit, the onset of reconnection occurs in roughly 2–6 light-crossing times, depending on the imposed driving timescale, which controls the duration of the thinning phase. In the subsequent nonlinear merging phase, the evolution becomes effectively independent of the initially imposed velocity, leading to magnetic-energy dissipation consistent with a normalized reconnection rate ∼0.1. Our results have important implications for explosive release of magnetic energy in magnetospheres of astrophysical compact objects and their surroundings.