A local alerted police after seeing the divers struggling in the water about 12.15pm as members of the public desperately tried to save the pair.
Ms Hanson was an Open Water diving instructor with Harbour Dive Australia in Mornington. The man was a less experienced diver, police said. Witnesses reported hearing Ms Hanson screaming for help from the water before she died.
Robert De Santis, the owner of a nearby restaurant, ran over to the pier to help.
He told Channel Nine News the woman was struggling to hold onto the other diver, who was unconscious, and yelling “hold him”.
“They had full gear on so it was very hard to hold them, we removed his gear to push the tank off,” he told the television network.
“She was sinking, I had to make the decision to let go of him and help her to the ladder…She was exhausted.”
Ms Hanson then slipped under the choppy water. It took search and rescue teams hours to retrieve her body from under the water due to the rough conditions.
Ms Hanson became a diving instructor in April last year.
Harbour Dive Australia wrote on its Facebook page at the time: “Harbour Dive has a new Instructor. Congratulations to Leonie Hanson on successful completion of her SSI Instructor Evaluation today in extremely difficult open water conditions”.
Sergeant Anthoula Moutis said police were investigating the circumstances surrounding the incident.
“The deaths are not being treated as suspicious,” she said.
Graheme McGillivray from Volunteer Marine Rescue said volunteer members were assisting police.
He said the deaths were “really upsetting”.
The pier is a popular scuba diving spot, but locals have described the weather on Friday as cold and “terrible.”
Wind speeds reached 30 knots (56km/h) in the early hours of the morning before dropping back to 15-25 knots for the rest of the day.
A local tourist operator said Mornington harbour was “at its worst in a north-westerly wind”.
Moderate north-westerly winds have been blowing since early Friday morning.