" Я БУДУ тебя ЖДАТЬ" is a sentence about the future.
Future actions in Russian can be expressed:
(1) either by the PERFECTIVE form of the verb:
-- я ПОДОЖДУ тебя;
-- я ПОДУМАЮ;
-- я ПРОЧИТАЮ эту книгу и ВЕРНУ ее тебе;
(2) or by the IMPERFECTIVE form of the verb:
-- я БУДУ тебя ЖДАТЬ (or я БУДУ ЖДАТЬ тебя, as It-ogo rightly explained);
-- я БУДУ ДУМАТЬ;
-- я БУДУ СМОТРЕТЬ этот фильм повторно;
-- я БУДУ ЧИТАТЬ каждый день на английском.
Your example " я БУДУ тебя ЖДАТЬ" has the verb "ждать" in the Future Imperfective form.
"БУДУ ЖДАТЬ" is, semantically, one action, and therefore one verb in the compound future tense-form,
but because it is compound in form (helping verb "буду" + the notional verb "ждать"),
equivalent to the English " I WILL BE WAITING for you", it may seem as if you have two different verbs.
The object of the verb "тебя" in your example is sandwiched between the helping verb "буду" and the notional verb "ждать".
It all depends upon your perspective: whether you analyze this sentence from the point of view of semantics, or syntax, or morphology.