Mr Morrison, who was prime minister between 2018 and 2022, wrote in an autobiography that he took medication to deal with "debilitating and agonising" anxiety during his tenure.
"My doctor was amazed I had lasted as long as I had before seeking help," Mr Morrison said in the book.
"Without this help, serious depression would have manifested. What impacted me was the combination of pure physical exhaustion with the unrelenting and callous brutality of politics and media attacks."
Mr Albanese, who defeated Mr Morrison at the 2022 election to take over as prime minister, welcomed the former leader's decision to speak publicly on the issue.
Anthony Albanese says Scott Morrison talking about his difficulties with anxiety is brave. (AP PHOTO)
"It was brave of Scott Morrison to talk in such a clear way about something that is so very personal and I think, 'good on him'," he told ABC TV on Monday.
"The truth is that the pressures of the job are substantial.
"Scott Morrison, I give him credit for being prepared to speak about such a difficult issue and I wish him well in his next phase of his life."
Mr Morrison resigned from federal politics in February after an almost 17-year career as an MP.
His resignation triggered a by-election in the southern Sydney seat of Cook, which was retained easily by Liberal candidate Simon Kennedy, who will be sworn into parliament in May.
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