"Two weeks ago I asked my soulmate to marry me and she said yes xx I am the luckiest man in the world. I promise to be the best husband and the best daddy one day I love you baby," Brooklyn, 21, captioned an outdoor photo of him and his new fiancee gazing lovingly at each other.
The post got more than 1 million "likes" since it was shared on Brooklyn's Instagram account early Saturday.
"You've made me the luckiest girl in the world," Peltz, 25, wrote in a message on her own feed. "I can't wait to spend the rest of my life by your side. your love is the most precious gift. I love you so so much baby and thank you harper for this pic."
The couple have been dating for about 10 months.
Fashion designer and former Spice Girls singer Victoria Beckham celebrated her son's happy news on social media, too.
"The MOST exciting news!! We could not be happier that @brooklynbeckham and @nicolaannepeltz are getting married! Wishing you so much love and a lifetime of happiness. We all love you both so much x @davidbeckham @romeobeckham @cruzbeckham #HarperSeven," Victoria wrote.
Victoria Beckham and soccer icon David Beckham are also the parents of Romeo, 17, and Cruz, 15, and Harper, 8.