The Australian revealed the happy news in an Instagram post, sharing a photo of the smiling couple embracing with an engagement ring on her finger.
"Future husband," wrote Barty, 25, who accompanied the post with a love heart and ring emoji.
Kissick, 30, is a former golf pro and the pair met on a course in Barty's home state of Queensland in 2016.
He is ever-present courtside when she plays and often posts supportive messages on social media.
The news sparked a frenzy of congratulations from fellow tennis stars, with Simona Halep posting 10 love heart emojis.
Reigning Wimbledon champion Barty pulled out of the season-ending WTA Finals to remain at home and focus on preparing for the Australian summer.
She has not played since a shock third-round loss at the US Open in September, but still finished as world No 1 after a season in which she won five titles.
Barty joined Steffi Graf, Martina Navratilova, Serena Williams and Chris Evert as the only women to finish as the top-ranked player for three consecutive years.