Cooper acquired a 65% interest in the Basker-Manta-Gummy permits from ROC Oil in 2014, and a number of wells were produced via the Crystal Ocean floating production storage and offloading vessel for the oil development.
The Basker, Manta and Gummy fields lie in the offshore Gippsland Basin, 56km south of the Victorian coast.
Basker was discovered in 1983 by Shell, followed by Manta in 1984.
The fields contain oil, condensate and gas.
The Basker and Manta fields first began producing oil in late-2005 but were more challenging to develop than first expected and production was interrupted on numerous occasions.
Atteris general manager Eric Jas said the company was pleased with the award.
"Decommissioning projects can be tricky," he said.
"The key to a successful project is employing the right people (expertise) on the job, taking a systematic approach to evaluate the risks, having the right processes in place, doing the required engineering studies and having a positive consultation process with key stakeholders," he said.
The decommissioning project will be led by Atteris' integrity management and decommissioning lead Allison Selman, who received Subsea Energy Australia's Special Recognition award at the group's recent event in Perth.
Selman has driven SEA's 12-month mentoring program, called WISE, to increase the level of gender parity in engineering within the subsea industry.
Cooper has 100% of the Manta gas field and in the nearby Sole gas field, for which front-end engineering and design studies have been completed. Cooper is looking at developing the Manta field directly after Sole.
Last month Cooper signed a contracted with revitalised Norwegian offshore vessel provider Solstad Farstad to provide the anchor handling tug and supply vessels Far Statesman and Far Senator to tow Diamond Offshore's Ocean Monarch semi-submersible drilling rig from the North West Shelf to the Bass Strait.
The vessels were due to continue with rig support duties for 120 days, and two lots of 60-day optional periods during the drilling of two Sole development wells and potentially an appraisal well, Manta-3.
Manta has a total of 227 petajoules of uncontracted gas, of which 106PJ is uncontracted 2C contingent resource at Manta, which also has more exploration potential which the company is looking to pursue as one of its growth projects.