Telstra said it would continue to invest in and operate the business across its six South Pacific markets - Papua New Guinea, Fiji, Nauru, Samoa, Tonga and Vanuatu.
Telstra International chief executive officer Oliver Camplin-Warner said the deal was an exciting milestone for the Digicel Pacific business and its customers in PNG.
"We're very pleased to welcome Digicel Pacific into the Telstra family," he said.
"The Digicel Pacific team in PNG have amazing local expertise and are leaders in digital experiences for their customers. Together, we'll work to ensure Digicel Pacific remains the top provider in PNG."
Camplin-Warner said there would not be any local job losses in the Pacific as part of the acquisition and the current Digicel Pacific team would continue the day-to-day running of the business.
"Digicel Pacific will still have the same people and products that their PNG customers know and love today," he said.
"Telstra will add to these strengths with our more than 100 years of experience building and operating the largest mobile network in Australia, and our operations in more than 20 countries worldwide.
"As part of our commitment to building a strong and sustainable PNG, Digicel Pacific will invest in an additional 115 towers which will be built across PNG over the next two years.
"This investment will mean continued improvements to 4G coverage, particularly in rural areas, which will bring with it opportunities to improve health, education, agricultural, commerce and cultural outcomes through the use of technology."
Digicel PNG chief executive Colin Stone said Telstra's expertise in rolling out world-class networks and connecting remote communities would greatly enhance the work to date of Digicel and benefit the people and businesses of PNG.
"Telstra has experience connecting regional and remote customers in challenging geographies across mountains, deserts, rainforests and coastlines," Stone said.
"We're looking forward to Telstra applying its network experience as well as its innovation and technology solutions to PNG to continue increasing connectivity in the region as Digicel has been doing for the past 14 years."
Camplin-Warner said the values of both Telstra and Digicel Pacific were a natural fit, with the companies committed to working together to build a connected future for everyone.