Some states may not care to know who the members of the LLC are (unless the LLC is member-managed), in which case you do not have to notify the state. However, if your state wants to know who the members are, or if the LLC is member-managed, then you must file a new list of officers with the state.
In any case, you must modify the LLC's operating agreement (and have a written notice sent to all existing members, depending on the protocol of your LLC, spelled out in the operating agreement) to add the new member, with the consent and signatures of all existing members.
In addition, yes, at the end of the tax year, the LLC will need to send a K-1 schedule to all members, new and old.