The announcement follows the appointment of managing director Chris Siniakov and director Andrew Canobi in May 2014.
Franklin Templeton said Ms Wee will join as a fixed-income research analyst and will have responsibility for credit research and analysis, while Mr Rout will join as a junior research analyst and trader.
Prior to her appointment, Ms Wee worked for Deutsche Asset and Wealth Management where she was involved in credit research for local Australian and offshore portfolio managers.
Ms Wee has also worked for Standard & Poor’s as a corporate ratings analyst.
Before Mr Rout’s appointment with Franklin Templeton, he worked for JANA Investment Advisers as an investment analyst where he was responsible for macroeconomic and asset allocation research for Jana’s implemented consulting business.