J-Power had offered 27.5 Australian cents per share for the renewable energy firm in which it already owns 7.7%.
The bid was backed by 83.54% of the proxy votes cast ahead of an investor meeting, according to a company slide shown at the meeting in Sydney on Tuesday, surpassing the requirement of at least 75% for the deal to proceed. A majority of individual shareholders backed the deal, the slide showed.
The final result of the vote will be known later on Tuesday.
J-Power, a major power generator with coal-fired power plants and hydroelectric facilities, deepened its 2030 emission reduction target last year by 1.3 million tons from 2013 levels.
The Japanese firm is a joint owner and developer of Genex's Kidston wind project and Bulli Creek clean energy project, which are both in the Australian state of Queensland.
The offer represented a 48.5% premium to Genex's share price in early March before the J-Power bid.
J-Power had originally offered 24 Australian cents, Genex said in March, before raising its offer to the level that was backed by the buyout target's board.
The bid was backed by Genex's largest shareholder Skip Capital, an investment firm founded by Atlassian co-founder Scott Farquhar, that holds 19.9% of Genex, local media reported on Tuesday.
