But the full phrase would be (if speaking to a male) Ты мне надоел!, right? Literally, "You (m.) have become tiresome to me!"
But Ты нам надоела! -- "You (f.) have become boring to us!" if several people are addressing a tedious woman.
In short, the verb agrees in number/gender with the person(s) who are tiresome, but the person(s) feeling the boredom is expressed by the dative.
And it's also common to use the verb impersonally: Мне надоело разговарывать только о футболе. ("I'm bored [it has become tiresome to me] of talking about nothing but football.")