There's a single word used quite often in such cases: "взаимно". That words is used when you want to express that you share the same feelings with person after he or she expressed that feelings. It could be used both for positive and negative sentiments. For instance:
Пётр: Как же я тебя ненавижу!
Василий: Знаешь, взаимно.
As of your phrase "я так же рад видеть вас" (notice that "так же" in this case is written separately) - it is a valid but slightly non-colloquial form. It sounds a bit pathetic. Something like "и я тоже очень рад" sounds more natural.