The 23-year-old Norway international arrives as Mark Hughes' second signing of the transfer window, following the capture of Stuart Armstrong from Celtic, and has penned a five-year deal at St. Mary's.
Elyounoussi has spent the past two seasons with Basel, scoring 23 times in 83 appearances and providing an additional 30 assists, and the Moroccan-born attacker is looking forward to developing in the Premier League.
"I'm really happy to be here and I am really excited to get started. The club has been following me for a long time, watching many games, so I feel really confident to come here and to get even better and develop myself," he told the Saints' official website.
Capped 16 times by Norway, Elyounoussi will be tasked with providing creative flair after the departure of Dusan Tadic to Eredivisie outfit Ajax earlier this week.
"Mohamed is clearly another very exciting addition to our attacking options," said Hughes about the new signing.
"He's still at a young age as well, so we're confident he can continue to improve and fulfil even more of his potential with us, and, following on from the arrival of Stuart Armstrong this week, we feel we have made real progress in adding a new dimension to our attack ahead of the season."