The photos, uploaded on Sunday, include a black and white image of Moore holding an infant Rumer Willis and an image of Rumer Willis hugging her mother on the set of 1996 film Striptease.
"Words can not do justice to the love, gratitude and joy I have for you. You are a magnificent woman but you will always be my baby," Moore said.
"You changed my life and gave it meaning beyond anything I had ever known. Happy Birthday, Rumer Glenn! I love you forever and a day," the actress continued.
Rumer Willis commemorated her birthday by posting on Instagram how she was spending her day outdoors.
"I am so excited for this year, my own personal New Years. This year I set the intention to let go of anything and everything that no longer serves me and trust that the universe is setting me up to have the life I have always dreamed of," Rumer Willis said.
Moore shares Rumer Willis, 29-year-old Scout Willis and 26-year-old Tallulah Willis with ex-husband Bruce Willis. Moore and Bruce Willis spent time together with their daughters in April amid the COVID-19 pandemic.