Joseph Baena just graduated from college ... and his old man is beaming with pride.

Arnold Schwarzenegger shared the news Saturday along with a happy photo of the 2, saying ... "Congratulations Joseph! Four years of hard work studying business at Pepperdine and today is your big day!"

He added ... "You have earned all of the celebration and I’m so proud of you. I love you!"

Arnold and Joseph have been tight the past several years -- even working out together -- but as far we know, Arnold's kids with Maria Shriver -- Katherine, Christopher, Christina and Patrick -- have never had a relationship with him.

Doesn't look like any of them were at the graduation either ... but that's not going to spoil the moment for father and son.