The CSI: NY star, who has been dating Ochse for two years, popped the question on New Year's Eve, E! News reports.
The couple were on vacation in Turtle Bay, Napili with Buckley's mother and Ochse's sister when the actor proposed.
The setting is said to be meaningful to Buckley as it is where he scattered the ashes of his late father, who passed away last year after suffering from pancreatic cancer.
Buckley reportedly hid the ring - said to be in a vintage style - in a box of fireworks before proposing.
The actor plays Adam Ross on CSI: NY and has also appeared on Supernatural.