Four gas wells and one oil well will be drilled by a rig on the field's new Marlin B platform with the program expected to continue into the second half of 2015.
Exxon said the Turrum field holds an estimated 1 trillion cubic feet of natural gas and 110 million barrels of oil and gas liquids.
"ExxonMobil continues to invest in Bass Strait to unlock new resources and maintain gas supplies," ExxonMobil Australia chairman Richard Owen said.
With Exxon recently abandoning its CSG-targeting Victoria Natural Gas joint venture, he took the opportunity to comment on policy challenges.
"In order to remain competitive in the region, Australia must pursue policies that continue to promote the development of our natural resources," he said.
"Streamlined regulatory approvals, long-term access to offshore acreage, productivity gains and competitive work practices are all required to create an environment that is conducive to further investment."
The Turrum and Tuna fields are owned by the Gippsland Basin joint venture (50:50 Exxon and BHP Billiton) while the Kipper field is a Santos (35%), Exxon (32.5%) and BHP (32.5%) JV.