The actress and the producer of "A Star is Born" -- the 1976 and 2018 versions -- and "Flashdance" ... got married Monday in a private ceremony in Malibu.

As for why the surprise, quickie wedding? Jon says, "There are beautiful girls everywhere. I could have my pick, but -- for 35 years -- I’ve only wanted Pamela. She makes me wild -- in a good way."

The couple dated more than 30 years ago, but their relationship came full circle in recent months. We're told they've remained flirty forever, and reconnected after she broke things off last year with French soccer star Adil Rami.

Jon told Hollywood Reporter, "Pamela has never seen her full potential as an artist. She has yet to shine in a real way. There is much more to her than meets the eye, or I wouldn’t love her so much."

The marriage marks the fifth for both Anderson and Peters. Pam's ex-husbands include Tommy Lee, Kid Rock and Rick Salomon ... twice.

Peters' exes include Lesley Ann Warren and Christine Forsyth-Peters, and he also dated Streisand for years.

Pamela also has some words about her surprise marriage, in the form of a poem. She writes ... "Jon is the original ‘bad boy’ of Hollywood - no one compares. I love him deeply like family. His life used to scare me."

She adds ... "We understand and respect each other - We love each other without conditions. I’m a lucky woman. Proof God has a plan”