Gillan and Lim have been co-lead managers on the trust for roughly six years, however when Gillan leaves Aberdeen in mid-December, Lim will take over the named lead role.
Gillan will be based in Henderson's Singapore office.
The wider Aberdeen Asian equities team – which includes veteran investor Hugh Young – will continue to manage the £567m trust.
Over the last five years Edinburgh Dragon’s share price has risen by more than 170%, and its board said the vehicle would be “unaffected” by the change. Investors were told that more than 40 equity managers helped run the fund, and many of these individuals have more than a decade’s experience working with Aberdeen alone.
Gillan is understood to be joining Henderson, to run its £200m Asia Pacific Capital Growth and Horizon Asia Growth funds.