According to Wikitionary, the Latin word verb is derived from the Proto-Indo-European word *werdʰh₁om which is the etonym of the English word word and the German wort. I am familiar with Grimm's Law which would explain why the PIE and English words have a d, while the German word has a t. But is there a specific law or rule that explains why the Latin derivation of this PIE word would have a b instead of a d?
User6726 explained why this sound change happened, but I'd like to explain more concisely what happened.
In the history of Latin, PIE *dʰ within a word usually became d, but instead became b next to r or u, and before l. This probably happened somewhere between Proto-Italic and Latin, where the outcome of word-internal *dʰ is usually reconstructed as *ð (that is, some sort of voiced fricative) that could have become *β (a labial voiced fricative).
Thus, PIE *medʰi-o- > PIt *meðio- > Latin medium, but *werh₁-dʰh₁-o- > PIt *werðo- > *werβom > Latin verbum.
In Oscan and Umbrian, on the other hand, all instances of *ð got labialized, regardless of what was around them. So the Oscan cognate of medium is mefio < *meβio-.
The "name" for the rule is labialization, though unlike names like Grimm's Law, Meinhof's Law and Osthoff's Law, it refers to a class of similar phenomena (likewise palatalization, lenition, vowel harmony). Typically, linguists are more interested in why a certain thing happened, though in some schools of linguistics you don't ask why, you just ask what.
The most likely explanation relates to acoustic and perceptual properties, not articulation. The consonants d and b differ acoustically in their formant frequencies, with b having a lower frequency. The acoustic-perceptual explanation is then related to the greater formant lower effect of u and r, both being strong formant-lowering segments. The fact that it affects dʰ and (generally) not d suggests (as do other facts of Latin historical phonology) that PIE voiced aspirates may have spirantized (see other spirant outcomes of the voiced aspirates). It is an interesting puzzle as to why *dw also labializes, but this is not too surprising since w is an even stronger formant-lowering segment compared to u.