I'm not sure the phrase "с 1999 по 2002 годы" is the best way of saying it. I think the concept becomes easier when you actually try to spell it out:

С тысяча девятьсот девяносто девятого [года] по две тысячи второй [год]. So, depending on how busy you are, you can skip either the first "год" or the second "год" or both.

I think the phrase "с 1999 по 2002 годы" can intuitively be attributed to the fact that:
С года Х до года Y проходят годы.

I think a much better version would be: "В годы с 1999 по 2002 ..." = "В годы с 1999-го по 2002-й ..."