The pro wrestling icon tells TMZ Sports ... he and Sky Daily got engaged last week, with Hogan popping the question at a restaurant in Tampa, Florida.

Hogan tells us he was very nervous about proposing ... but Sky said, "Yes."

The WWE Hall of Famer says his fiancée has three children of her own, and he fell in love with all of them.

As we reported, Hogan and Sky, a yoga instructor, started dating early last year ... with Hulk moving on quickly after his divorce from his second wife, Jennifer McDaniel, was finalized.

We broke the story ... Hulk also had to buy Jennifer a new car as part of the divorce settlement.

Hogan and Jennifer were married for over 10 years, tying the knot in 2010 after he split from his first wife, Linda Hogan.

Now, Hulk's heading for his third marriage.