Vittorio Missoni, 58, and his wife were among six people on board the flight from Los Roques islands to Caracas.
Interior Ministry spokesman Jorge Galindo announced the discovery of the plane on Twitter.
Officials said it was found 230 ft under water, north of Los Roques islands in the Caribbean.
Following the plane’s disappearance on January 4, investigators from the Italian Agency for Air Safety (ANSV) said the company that owned the small plane was not fully licensed to operate.
A piece of luggage from the aircraft was found off the Dutch island of Curacao, about 200 miles west of Los Roques, later that month.
Vittorio Missoni was the son of the fashion brand’s founder, Ottavio Missoni, and co-owned the firm with his siblings.
He was returning from a Christmas and New Year holiday with his wife, Maurizia Castiglioni, and two friends – Elda Scalvenzi and Guido Foresti.
Two Venezuelan pilots were also on board the BN-2 Islander plane.
Minutes after take-off, one of the pilots reported that the plane was at 5,000ft and 10 nautical miles from Los Roques airport, Italy’s air safety agency has said.
The last radar report showed the aircraft accelerating at 5,400ft before it rapidly lost altitude and speed, veering to the right until it disappeared from the radar.
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