The pair, who play Summer Bay couple Rachel Armstrong and Tony Holden, are expected to bow out on screen in the middle of the year.
A show source told Australian magazine TV Week: "Amy Mathews is definitely going in a few months' time. Then, with Amy's character Rachel out of the picture, it was decided Tony should go with her, so Jon Sivewright is leaving too."
The news follows a number of recent high-profile Home and Away exits, including those of Lincoln Lewis (Geoff Campbell), Todd Lasance (Aden Jefferies) and Jodi Gordon (Martha MacKenzie).
However, a representative for Australia's Seven Network, which broadcasts Home and Away, insisted that viewers should not be concerned about the large number of recent cast departures.
Seven's Bevan Lee told fan site Back To The Bay: "There have indeed been a larger than usual number of characters being written out in the last few years, but the vast majority of those departures were brought about by the choices of the actors playing the roles.
"The fans can rest assured that no character is ever written out without the greatest of thought and consideration being given to the decision. They simply have to trust the creators of the show, trust their love for the show and accept that we would not make any choice we did not feel was for the best for Home and Away in the long run."