Opinion polls in Australia had all pointed to a Labor victory ahead of Saturday’s vote.
Mr Morrison, however, cast himself as the candidate who would work for aspirational voters and the tactic seemed to strike a chord.
«I know that under your leadership the great friendship between Australia and Israel will grow even stronger,» Mr Netanyahu said to Mr Morrison on Twitter.
Australia formally recognised west Jerusalem as Israel’s capital last year, reversing decades of Middle East policy and following Trump’s decision to move the US embassy to Jerusalem from Tel Aviv.
Mr Morrison has also been in touch with US Vice-President Mike Pence and had contact from the UK.
He was expected to speak to Prime Minister Theresa May on Sunday afternoon.
French President Emmanuel Macron and New Zealand Prime Minister have also offered congratulations directly as have former New Zealand prime ministers John Key and Bill English.