Arnold Schwarzenegger to Son -- Happy Birthday ... Let's Work It Out!

Arnold Schwarzenegger's son Joseph Baena is turning 16 today ... and he's getting the perfect gift from his dad -- A COMPLETE HOME GYM ... TMZ has learned.

In case you haven't noticed, Joseph is a behemoth -- a virtual carbon copy of a very young Austrian immigrant ... and Arnold clearly feels the apple may not fall far from the gigantic redwood tree.

Although Joseph lives with his mom in Bakersfield ... we've learned Arnold has established a very close relationship with the boy. They talk regularly on the phone and Arnold has flown him to several premieres.

As one source put it, "Once the truth came out, Arnold embraced Joseph. Since then, they've been slowly building a great relationship."

FYI -- Arnold started pumping iron around the time he was 16 and he quickly blew up to become Mr. Universe. So, current Mr. Bakersfield ... watch your back!