The model's parents David Beckham and Victoria Beckham, gave their blessing to the happy couple who confirmed their relationship in January.
Brooklyn, 21, wrote on Instagram: "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 xx."
She replied: "I'm so lucky to call you mine."
They posted the same picture of themselves standing in a field and embracing, with her wearing a yellow dress and him in a blue suit.
Peltz, 25, wrote on her Instagram: "You've made me the luckiest girl in the world.
"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."
Friends and family quickly congratulated the couple, with Brooklyn's parents posting the same photo and saying it is the "MOST exciting news" and they could not be happier they are getting married.
F1 driver Lewis Hamilton wrote: "Congratulations bro."
Actress Millie Bobby Brown said: "Congratulations!! So much love."
Brooklyn is the eldest of the Beckham's four children while Peltz, who is from New York state, has been in films including "The Last Airbender" and "Transformers: Age of Extinction".