In one aspect, a system for controlling the position of an agricultural implement being towed by an agricultural vehicle may include first and second wheels and first and second non-contact-based braking devices. As such, the first braking device may be configured to apply a braking force to the first wheel, and the second braking device may be configured to apply a braking force to the second wheel. Furthermore, the system may include a controller configured to control an operation of the first braking device or the second braking device when it is determined that the position of the implement differs from a predetermined position for the implement such that the braking force is applied to the corresponding wheel in a manner that adjusts the position of the implement towards the predetermined position.