The rig was part of Woodside's Vincent oil field development campaign and the last flight to evacuate the men on a 16-passenger capacity helicopter was aborted for safety reasons, with the stormy weather dangerously impacting visibility to carry it out.
While the incident has triggered various criticisms from a union official on Friday, the stormy conditions were not strong enough to interrupt communications from the rig.
"The 16 personnel who remained on the rig were safe and secure throughout the cyclone and in regular contact with the mainland," Atwood said this morning.
"Atwood Oceanics can confirm that all its operational crews are back on the Atwood Eagle and all non-essential personnel will be returning to the rig during today."
An inspection of the rig also confirmed there was no material damage to the rig.
The Eagle rig also held its position, unlike the Atwood Osprey rig that was blown off its moorings by
Tropical Cyclone Olwyn in March.
"The rig remains fixed on location and the well is secured in line with standard cyclone preparation procedures," an Atwood spokesman said in an earlier update.
"Atwood will review the de-manning procedure for Tropical Cyclone Quang to ensure that all actions were undertaken in an appropriate and timely manner.
"The health and safety of all personnel aboard an Atwood rig or any contractors servicing the rig is of paramount importance to the company."
While Quang was at a Category 3 intensity at sea on Friday morning, it effectively fizzled out by the time it made landfall.