Wallabies halfback Genia is out of contract and expected to join the exodus of Australian players heading to Japan after the World Cup, leaving a big hole in the Rebels' backline.
Lomani, 23, was Player of the Year in Australia's third-tier National Rugby Championship in 2018 after guiding the Fijian Drua team to last year's title.
He has been capped eight times for Fiji, including the shock 21-14 win over France in Paris in November.
"Signing with the Melbourne Rebels is a dream come true for me," Lomani said in a team statement on Friday.
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"I've played against many of these guys before, so to line up alongside them will be special."
The Rebels finished second in the Australian conference but missed out on the playoffs for a ninth season in succession.
(Reporting by Ian Ransom; Editing by Sudipto Ganguly)
