The overburdened sheep, named Baarack, had been found "wandering in the rugged Victorian bushland" by a property maintenance man who took it to Edgar's Mission in Lancefield, Victoria, in early February, the shelter said.
In the video filmed by staff at Edgar's Mission on February 5, Baarack struggles to balance himself under the weight of his matted and dirty fleece.
"This is a good place to be, ole' mate," a man is heard telling the sheep.
Edgar's Mission told Storyful that Baarack was "doing so well" and accustoming to life at the shelter.
He had more than 35 kilos worth of wool off him, according to CNN.
"We truly believe that he understands what we have done for him has eased his life and turned it for the better," they said. "For the time being he is setting in with equally lucky other rescued sheep."
Baarack's before-and-after photos have gone viral online.
In case you didn't know, sheep need humans to trim their wool. If it's left to grow unchecked, it's bad for their health.
Storyful and CNN contributed to this article.