In a statement posted to the ASX after it closed on Friday, VHA said it had filed a statement of claim to seek approval for the proposed merger.
The Australian Competition and Consumer Commission announced on 8 May, a day ahead of the scheduled date for its final decision, that it would be opposing the proposed merger between the two companies.
Both firms said the same day that they intended to challenge the decision in court.
TPG's statement to the ASX said: "For legal process reasons, the Statement of Claim identifies VHA as the applicant and the Australian Competition and Consumer Commission and TPG as the respondents.
"TPG and VHA are working together to progress the proceedings and TPG supports the orders being sought in the VHA application. The parties will seek orders for expedition of the proceedings."
As to the reasons for its decision, the competition watchdog said it had considered that the proposed merger would reduce competition and contestability in the fixed broadband sector.
It said, in particular, a deal was likely to "substantially lessen competition in the supply of mobile services because the proposed merger would preclude TPG entering as the fourth mobile network operator in Australia".
The proposed merger was announced on 30 August last year, with the scrip deal creating a company with an enterprise value of about $15 billion.