The rehabilitated birds were fitted with satellite tracking devices and released into their Perth Hills habitat last week as part of a trial research project between Murdoch University, the Department of Environment and Conservations (DEC) and Perth Zoo.
Kris Warren and Dr Anne Le Souef from Murdoch's conservation medicine program oversaw the release and are monitoring the cockatoos.
"There is limited information about the daily habits of these birds so we are incredibly excited about the data we're starting to gather in this trial," Dr Warren said.
"Initial reports are telling us that the birds have been flying around the Kelmscott area where they were released on Friday, and have stuck together, which is good for their continued well-being.
"They have been actively exploring the area within several kilometres around the release site. The two birds are estimated to have each flown a distance of approximately 15 kilometres over the last two days, and have been roosting in known roost sites in the area.
"The more we can learn about the distribution of this endangered species, the better informed we will be to help manage their recovery."
Dr Warren said it was the first time Baudin's cockatoos had been tracked in this way. The project follows on from a similar initiative to track 11 Carnaby's cockatoos.
The Baudin's cockatoo is one of three endangered black cockatoo species which is endemic to south-west Western Australia and are found in the southern eucalypt forests of jarrah, marri and karri trees.
Habitat destruction, poaching, vehicle strikes and feral bees present are major threats to the species.