Mr Albanese, 60, and Ms Haydon, 45, met at a Melbourne business dinner in 2020.
A number of Australian politicians congratulated the couple on their engagement, as well as British celebrity chef Nigella Lawson.
“Love is a beautiful thing. I’m so happy for you both!” Australian Foreign Minister Penny Wong posted.
However, online critics suggested Mr Albanese was trying to distract from pressing issues, including the war in Gaza.
Mr Albanese is the first Australian prime minister to get engaged while in office.
He was previously married to Carmel Tebbutt for 19 years, before they divorced in 2019. They had been together for a total of 30 years and share a son, Nathan.
Mr Albanese, nicknamed “Albo”, joined the centre-left Labor Party while in high school and later became deeply involved in student politics at the University of Sydney.
He was sworn in as prime minister in May 2022.