"Thanks for all the congratulations everyone, I'm a very happy lady indeed and all the warm wishes are well appreciated! We plan to keep our special day very private and we hope everyone can respect that. Thanks for the love, right back atcha!" Grimes wrote.
E! Online said the couple has been dating since last spring.
Grimes, who plays Annie Wilson in the hit show "90210," starred in the movie "Scream 4," the Daily Mail reported.
Beech has modeled clothes for Burberry, Just Cavalli and Levi's 501 Jeans.