Their engagement comes two years after Anna and Michael, 48, who worked on the movie Overboard together, began dating.
The actress has been married twice before, and reflected on this on an episode of her podcast, Anna Faris Is Unqualified.
She spoke of her of her new relationship with Michael, and also reflected on her divorce from Chris Pratt, with whom she shares her son, Jack, and her previous divorce from first husband Ben Indra.
"This is a tricky area for me because I've gone through two divorces now," she said of the relationship theme of the podcast episode.
"I'm in an amazing relationship, I do want to talk to everybody about these things, that I don't really know much about. But I also feel that I want to protect things in a way that I hadn't considered before."
Chris Pratt, 40, and Anna were married for eight years before announcing their separation in 2017.