"We got engaged two weeks ago," Bristol, 19, tells Us Weekly. "It felt right, even though we don't have the approval of our parents."
Palin gave birth to son Tripp in December 2008.
They say they hid the engagement news from Sarah Palin.
Sarah Palin released a statement on "Today" Wednesday morning: "Bristol at 19 is now a young adult. We obviously want what's best for our children. Bristol believes in redemption and forgiveness to a degree most of us struggle to put in practice in our daily lives."