They are both correct, in Spanish is not really necessary to say who does an action or say something all the time because the way you conjugate the verb tells you that. Let me give you an example of the conjugation of the verb amar (to love) I love = yo amo you love = tú amas (singluar) she/he loves = ella / él ama we love = nosotros amamos you love = ustedes aman (plural) they = ellos aman If you see the only pronoun which has the conjugation of amar as "amo" is Yo (I), that's why you can say it either way "Yo te amo"(adds a little emphasis) or just "te amo" (more casual) It gets confusing however when you just say "te ama" (loves you) as both he and she share that form so if the receiver of the love has no idea who they are talking about, it would be better to say Ella te ama (She loves you), Él te ama (He loves you) or (Name of the person) te ama, so they can have an idea.

Everybody has already told you that both are correct, however, I would like to emphasise that in spanish we omit pronouns most of the time. It would sound a little bit weird if you used pronouns all of the time. As Mike said, using a pronoun gives more emphasis, in this case, to the subject. I disagree a little with Mine: "Te ama" is quite ambiguous out of context, however in a conversation you would really know whom you are talking about.

"Te amo" it's correct...

Both yo te amo and te mo are correct. Usually, we use verbs without pronouns in the spanish language but sometimes we need them to emphasize, for example, our feeling.

Both forms are correct, the difference is that "Yo te amo" have an explicit subject and "Te amo" have an implicit or tacit subjec, this is the form that to name this phrase I hope that this help you I don't know to much english but i try to do it the better than I can