It's not irregular but all you can do is just to memoize such cases.
т happens in some verbs like "плести"/ "плету", "цвести"/"цвету", "мести"/"мету" for instance, a change to
д is not that rare as well, check out for instance:
- блюсти / блюду
- брести / бреду
- красть / краду
- прясть / пряду
So it's not something exotic. Here's a small explanation I borrowed from this book:
"Der Infinitiv läßt das nicht erkennen, da nach slavischen Lautgesetzen д, т vor "т" zu c wurden"
Or, in my free translation - the infinitive doesn't indicate this because, due to Slavic sound law
c, so "вести" was initially "ведти" and what you've found are the traces of that old spelling.
This is, by the way, the case in all examples mentioned above. If you take a closer look you'll see that 'красть' was derived from "*kro-d-" stem, "блюсти" can be traced to Proto-Indo-European *bʰewdʰ-, "брести" is from " *bʰredʰ-." and "прясть" we got from "*prędti".
The scientific term for this changes is "the assibilation of dental stops". The last thing I want to add that this happens very likely in Pre-Slavic since Slavic languages share such similarities with Baltic languages.