Barty shared a post on Instagram with the caption "Future husband", along with a picture of the pair in which she is wearing an engagement ring.
Kissick, a trainee golf professional in Queensland, shared two photos on his Instagram page with the date November 15 and the caption, "I love you @ashbarty".
The pair met in 2016 at Brookwater Golf Club and while their romance has been low-key Kissick has been supporting Barty at various tennis tournaments.
The announcement comes soon after Barty joined Serena Williams, Steffi Graf, Martina Navratilova and Chris Evert as the only players to finish year-end No.1 for three-straight years.
Barty, 25, won five WTA singles titles in 2021 including a maiden Wimbledon crown.
She opted not to play in the WTA finals in Mexico to return home to prepare for next year's Australian Open.
A host of sporting organisations, fellow tennis professionals and athletes via social media were quick to congratulate Barty and Kissick after their happy news was made public.
They included the Tennis Australia, the Australian Open, the WTA, Richmond AFL club, Samantha Stosur, Stephanie Gilmore, Aaron Finch and Barty's former doubles partner Casey Dellacqua, who wrote "Best news EVER beautiful couple".