Both are correct. If Google Ngrams can be believed, "served as chairman" has been more common for a long time.
But be aware that "chairman" may have sexist connotations. Unless you have a good reason not to do so, I recommend "served as chair." Google also indicates that this genderless version has gained popularity in the last few decades.
On a side note, use "has served" with "since." With the simple past that you have chosen, you would be more likely to write something like this:
He served as chair of the committee of the festival from its origin until 2019.
The following is more succinct and eliminates the repetition of "of":
He chaired the committee of the festival from its origin until 2019.
Obviously, such a change alters the nature of my response. There is nothing inherently wrong with "served."
Should "Committee of the Festival" be capitalized as I show it here? If that its official name, then the caps are probably required.