Thomas, who will become Ardent Leisure's chief customer officer and chief operating officer (Australasia), steps down half a year after Kate Goodchild, Roozi Araghi, Luke Dorsett and Cindy Low were killed at Dreamworld.
"During Deborah's leadership our company has experienced an unprecedented level of reorientation and change and has positioned itself strongly for solid future growth," Ardent Leisure chairman George Venardos said this week.
Shares in the company rose slightly on the news that Thomas was leaving.
New boss Kelly earned more than $300,000 in the 2016 financial year - more than any other executive in Australia - but will take a pay cut in his new role.
Chief financial officer Richard Johnson also quit the company, for personal reasons.
Six passengers were in a raft on the Thunder River Rapids ride in October last year when it collided with an empty raft that had become stuck.
Two children were flung to safety from the raft as it hit the other, but the four adults landed on a conveyor belt.
Two of them were crushed by the belt while the other two drowned in the water below.
The ride has since been decommissioned.
The park has been beset with issues since, with profits plummeting as fewer families visit.
In early January, Ardent Leisure released a statement revealing Dreamworld ticket sales had dropped to A$3.66 million ($3.97m) - down 63 per cent - in just 21 days over December.
Over the same period in 2015, the park raked in A$9.89m in ticket sales.
Dreamworld is believed to have suffered a loss of A$10m in the six weeks it was closed as a review of safety at the park was completed.
The park has also had issues with its rollercoasters stopping mid-ride in recent weeks.
In January - just a month after Dreamworld reopened following the four deaths at the park - one of the rides shut down, leaving park guests dangling 119m above ground.