Klim joined Bravura three years ago as the chief executive for Europe, Middle East and Africa and will be based in the company's London office.
During his time as chief for Europe, Middle East and Africa he expanded the regions both through organic and acquisitive growth, with Europe accounting for almost 70 per cent of the company's revenue.
"We are extremely pleased to appoint Tony to the position of group chief. Tony has a wealth of experience in international financial services, having held a number of executive and board positions with private and listed companies in this sector over the past 25 years," Bravura chair Brian Mitchell said.
Commenting on his appointment, Klim said: "I believe that Bravura is in a strong position to move forward as a market-leading provider of transfer agency and wealth management software applications to the financial services market.
"While I am extremely familiar with our European clients and employees, I am looking forward to spending more time in Australia, New Zealand and Asia to get to better know and understand the needs of our wealth management clients and employees in our home base."
Klim starts his new job immediately.
His appointment follows the departure of the company's co-founder and chief, Simon Woodfull, in April.
Mitchell said Woodfull would no longer be a part of the company in any regard.
His departure comes less than a month after the Bravura board rejected unsolicited offers to acquire all of the issued capital of the group, with the company's board confident in the strategy and direction of the business.