Sources close to the reality TV star tell TMZ ... he's engaged to his new girlfriend, Francie Frane, and they are very happy and looking forward to a long life together.

We're told Dog's kids are supportive of the relationship ... which was not the case the last time around.

As you'll recall ... Dog quickly got involved with Moon Angell after the death of his wife, Beth Chapman, which led to some family turmoil when they began living together.

Dog shockingly proposed to Moon in bizarre fashion on "The Dr. Oz Show" in January, but it was chalked up to him just being overly emotional ... and never led to an engagement. Moon later moved out.

Dog and Francie apparently began dating after that, and he proposed to her recently at his Colorado home -- as was first reported by The Sun --and she said yes!

He's reportedly said he wants to have "the biggest wedding there's ever been" with Francie and open it up to all his fans.

We broke the story ... Dog's wife, Beth, died in June after a long battle with cancer.