She penned: "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."
The confirmation comes after a source claimed the couple were engaged and his parents, David and Victoria Beckham, had given their blessing.
An insider said of the happy couple's big news: "Brooklyn has been telling his friends in LA that he and Nicola are engaged. It's common knowledge among their group of friends. They are smitten."
"David and Victoria have very much given this relationship their blessing. It's a very exciting time for the whole family and after a few previous rocky relationships, they think Brooklyn has landed on his feet."
Brooklyn Beckham recently posted a series of photos of him and Peltz running through a field at sunset, and wrote: "My beautiful angel". In an image from April, he declares he will "always" be by Nicola's side, and in another, he calls her his "other half".
Victoria Beckham could "not be happier" for her son
The fashion designer paid tribute to her 21-year-old son and his fiancé Nicola Peltz as the couple announced their happy news.
Taking to Instagram, Victoria wrote: "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."
Responding to her comment, Peltz shared: "I love you so so much victoria i'm the luckiest girl."
