The 1946 statute gave CBP the authority to stop and search all vehicles within a “reasonable distance”. CBP defined the reasonable to be 100 miles and it stuck. It's just federal regulation interpreting the law and courts have blessed it.

Supreme Court rulings it seems. This is the law: https://www.law.cornell.edu/uscode/text/8/1357#

But it only says "any reasonable distance". SCOTUS appears to have come up with the 100 mile limit in various cases over time.