The announcement on Thursday, made by Prime Minister Malcolm Turnbull during a visit to London to attend the Commonwealth Heads of Government Meeting, comes in the wake of January's announcement by the Vocus Group that it had entered into a deal with the federal government to undertake a scoping study on design, construction and procurement for the cable system.
Turnbull said: "Today we affirm our commitment to deliver a high-speed undersea telecommunication cable between Australia and Solomon Islands.
"Australia will deliver and majority fund the project as part of a cable system that will connect both Honiara and Port Moresby to Australia, with a financial co-contribution from both Solomon Islands and Papua New Guinea. It is scheduled for completion by the end of 2019.
"Ensuring stability, security and prosperity in the Pacific is one of the highest priorities of our two nations. Boosting connectivity in Solomon Islands will improve governance and security, and drive economic growth.
"Increased connectivity also exposes countries to risk. Through the Cyber Co-operation Program, Australia is working with Solomon Islands to manage these risks by strengthening its cyber security architecture and combating cyber crime."
A Huawei spokesperson said the company had no comment.
The undersea cable was initially budgeted to cost US$70 million and was to be funded by the Asian Development Bank. But then, after the Solomon Islands Government said Huawei would build it, the ADB withdrew, citing concerns over transparency.
Last July, it was reported that Australia was putting pressure on the Solomon Islands to withdraw from the Project Honiara undersea cable project after the contract was awarded to Huawei.
Security concerns were said to be the reason why Australian officials had made the request which was, tellingly, conveyed to Solomon Islands Prime Minister Manasseh Sogavare by Nick Warner, the director-general of the spy agency ASIS.
In the US, Huawei has faced problems as well with a deal for AT&T to sell the Chinese firm's phones on plans being cancelled by the American company at the last minute in January.
Not long after, Verizon was reported to have yielded to pressure from the US Government to stop selling Huawei devices.
In February, US intelligence chiefs warned against the use of Huawei equipment. And last month, Republican Congressman Michael Conaway cautioned that the US-Australia relationship could be damaged if the Chinese vendor was involved in building 5G networks Down Under.
Back in 2012, the US Congress issued a report that raised concerns about state-sponsored spying related to products made by Huawei, the biggest global maker of telecommunications equipment. The company has denied any such involvement.
More recently, the Federal Communications Commission said it would move to prevent Huawei, and another Chinese telco, ZTE, from receiving any subsidies from the Universal Service Fund that the US uses to subsidise equipment bought by rural and small carriers. Huawei is reportedly cutting back US sales efforts as a result.
Six years ago, Huawei was denied any role in supplying equipment to Australia's national broadband network project, following advice by ASIS, one of Australia's spy agencies.