It said 50.1% of the merged entity would be owned by Vodafone with the remainder to be owned by TPG.
Last week, the two companies confirmed that they had engaged in exploratory talks, issuing identical statements to the Australian Stock Exchange on 22 August.
Local telecommunications sector incumbents like Telstra and Optus have been awaiting the entry of TPG into the mobile sector with some trepidation as it would add a fourth player to an already crowded space which has taken a beating from the rollout of the NBN.
The statement said TPG's chief executive David Teoh would be the chairman of the merged entity, while Iñaki Berroeta, the head of Vodafone, would function as chief executive.
The board of the merged entity will comprise Teoh, Berroeta, TPG directors Robert Millner and Shane Teoh, two nominees each from TPG and Vodafone, and two new independent directors.
It said Vodafone had about six million mobile subscribers at the moment while TPG had a fixed-line subscriber base of 1.9 million.
Vodafone is expected to have net debt of $1.9 billion on 31 January 2019 while TPG brings net debt of $1.7 billion, plus an $80 million spectrum instalment due on 31 January 2019.
Vodafone New Zealand will not be part of the deal while Vodafone Australia will demerge its Singapore mobile unit. No equity will be raised by TPG as part of the deal.
Teoh said: "The merger... represents an exciting step-change in TPG's evolution and will benefit both our shareholders and Australian consumers alike."
Berroeta said: "The Australian telecommunications market is characterised by the presence of Telstra and Optus. Together TPG and VHA will provide stronger competition in the market and greater choice for Australian consumers and enterprises across fixed broadband and mobile."
In April last year, TPG paid over the top for two lots of 10MHz in the 700MHz spectrum auction, forking out $1.2 billion, and said it planned to roll out a $600 million mobile network.
And in May this year, the company announced that it would a free, unlimited mobile data plan on its first mobile services in the third quarter of 2018.
While Vodafone's mobile subscriber numbers have been growing, it has also been suffering big financial losses, according to its FY2018 results.
You can listen to the full audio of Vodafone and TPG's teleconference call for media and analysts this morning in iTWire's article entitled "FULL AUDIO: Vodafone and TPG merger call as Voda promises 'great value' for customers".