The highly anticipated deal is expected to relaunch Versace's fortunes after middling post-pandemic performance as part of the US luxury group Capri Holdings.
Prada said on Tuesday that the acquisition had been completed after receiving all regulatory clearances.
Prada heir Lorenzo Bertelli will steer Versace's next phase as executive chairman, as well as his roles as group marketing director and sustainability chief.
The son of co-creative director Miuccia Prada and longtime Prada Group chairman Patrizio Bertelli has said he did not expect to make any swift executive changes at Versace.
But Bertelli has said the company, which places among the top 10 most recognised brands in the world, has long been underperforming in the market.
Prada has underlined that the 47-year-old Versace brand offered "significant untapped growth potential'.'
Versace has been in the midst of a creative relaunch under a new designer, Dario Vitale, who previewed his first collection during Milan Fashion Week in September.
Capri Holdings, which owns Michael Kors and Jimmy Choo, paid $US2 billion for Versace in 2018, but had been struggling to position Versace's bold profile in the recent era of "quiet luxury".
Versace represented 20 per cent of Capri Holdings 2024 revenue of 5.2 billion euros.
An analyst presentation for the Prada deal said Versace would represent 13 per cent of the Prada Group's pro-forma revenues, with Miu Miu coming in at 22 per cent and Prada at 64 per cent.
The Prada Group, which also includes Church's footwear, reported a 17 per cent boost in revenues to 5.4 billion euros in 2024.
The Prada Group has already begun preparations to incorporate cross-town rival Versace into its Italian manufacturing system, a point of pride for the group.
"Making a bag for one brand or another, the know-how is the same," Bertelli told reporters last week at the group's Scandicci leather goods factory, which already makes bags for the Prada and Miu Miu brands and will soon add Versace.
