The cable will provide 72 Tbit/s of capacity between the cities and will be the largest and lowest-latency route connecting Australia, New Zealand and the USA.
In December, the cable landed in Sydney before finalising branch landings in Fiji.
Southern Cross worked in collaboration with management company Pioneer Consulting throughout the project.
Pioneer handled the dynamic elements of the project, including market and business case analysis, project implementation and quality assurance.
"We are tremendously proud to have completed this critical phase of NEXT's development in partnership with Pioneer Consulting," said Laurie Miller, CEO of Southern Cross Cable Network.
"Once activated, this high-capacity route will provide enhanced reliability and network efficiency from Los Angeles to Sydney, and all points between."
Being granted provisional acceptance of the project represents the material completion of the NEXT system marine programme, the company added in a statement.
The system was designed, manufactured and installed by Alcatel Submarine Network and is expected to be available for commercial service on July 7.