With the variant by the gender of the person who speak:
If the speaker is a man:
"También estoy orgulloso de ti"
If the speaker is a woman
"También estoy orgullosa de ti"
Also you can express:
'Yo estoy orgulloso / orgullosa de ti también."
You can use both.
My advice is the first option, sounds better.
Is used when someone has told you he or she is very proud of you, and you can express yo him /her you also are proud of him/her.