A study was performed to examine the Jc behavior as a function of thickness in MgB2 films fabricated by ex situ annealing at 840 °C of boron films, grown by chemical vapor deposition, in Mg vapor. The film thicknesses range between 300 nm and 10 µm. The values of Jc range from 1.2 × 107 A cm−2 for 300 nm to 1.9 × 105 A cm−2 for 10 µm film thicknesses at 20 K and self-field. The study shows that the critical current density (Jc) in MgB2 films decreases with increasing film thickness, similar to that observed in YBCO-coated conductors. Moreover, our study shows that critical current (Ic) reaches its maximum value of 728 A cm−1 width at ~1 µm thick MgB2 films at 20 K and self-field, which is, interestingly, the same thickness of pulsed-laser-deposited YBCO-coated conductors at which Ic reaches its maximum value. The high Jc values carried by our films show that the ex situ fabrication method can produce high quality MgB2 films at low processing temperatures, which is promising for RF cavity applications and coated-conductor wires and tapes.