Prime Minister Lee Hsien Loong has written to his Australian counterpart Malcolm Turnbull to congratulate him on the Coalition's return to government following elections.

Australia's ruling conservatives finally secured a parliamentary majority following a protracted election vote count, projections showed on Monday.

Mr Lee, in his letter to Mr Turnbull, wrote: "On behalf of the Government, I would like to convey my warm congratulations on your election as the Prime Minister of Australia.

"Singapore and Australia enjoy excellent relations. I deeply appreciated your support in concluding the Comprehensive Strategic Partnership which has further elevated our longstanding friendship into a deep and dynamic partnership."

Mr Lee noted that the pact would bring the two countries even closer in all areas, particularly in trade and investment, defence and security, and science and innovation.

Mr Lee concluded by extending the personal best wishes of his wife, Ms Ho Ching, and himself to Mr Turnbull and his wife, Lucy: "May you both continue to enjoy good health and every success in your endeavours."

The Liberal/National coalition, which declared victory on Sunday after the opposition Labor Party conceded defeat, won 76 seats in the 150-seat Lower House of Representatives, national broadcaster ABC said.

The tightly contested July 2 election followed three years of turbulence in Canberra, where two sitting prime ministers were deposed by their own parties in a "revolving door" of leaders.

Mr Turnbull is expected to swear in his new Cabinet next week with Governor-General Peter Cosgrove, reported Agence France-Presse.