Ivery proposed to the actress on Friday, which was also her 37th birthday, after breakfast at their home.
According to Pompeo's representative, "She was surprised and thrilled."
Ivery presented her with a 3.5-carat emerald-cut diamond in a platinum setting from jewelry designer Tacori.
Pompeo and Ivery, 37, are both natives of Boston and grew up minutes away from each other, but didn't meet until a pal introduced them in Los Angeles in 2003.
The pair began dating six months after their initial meeting, after developing a close friendship.
According to her representative, no wedding date has been set.
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