Cook posted a video to Instagram of Cuoco joyfully crying moments after he popped the question.
"What's on your finger, honey?" he asks.
"We're engaged," she replies.
He then points out that she hasn't said yes, and before he can finish the sentence she says "YES!"
He also posted a close-up of the ring from Nadis Diamonds.
He ended the string of posts with a video of him and Cuoco embracing and murmuring sweet nothings to each other. "In life, there is nothing like dancing right after getting engaged," he captioned it. "The purity and grace of the moment are inexplicable, it is truly as though life were a balloon bouncing on the smoothest zephyr. Honey; all I want is to be a balloon bouncing, bobbing, and flowing through life together. You are my everything."
Cuoco and Cook have been together since late 2015.
Cuoco was previously married to tennis player Ryan Sweeting. They divorced in 2016 after separating the previous year.