One Punch Man started life as a crudely drawn Webcomic created by ONE. It then went onto be discovered by (if I recall his name) Yusuke Murata of Eyeshield 21 fame, who re-drew it with explicit permission of ONE. Then it got turned into an anime series.
Even more directly, ONEs other series, Mob Psycho 100 was directly animefied last year, to much acclaim.
Relatedly, you have many, many light and net novels that have been turned into series of their own.
Now, this isn't precisely what you meant, but it's still a thing that I think is related.