The 31-year-old, who has won 59 Scotland caps, will join Wasps for the start of the new season after being ruled out of the forthcoming Rugby World Cup.
The former Bristol, Worcester and Edinburgh back was last week forced to withdraw from Scotland's provisional squad with a knee injury.
Southwell said: "I'm delighted to sign a deal with Wasps and am really keen to get started. I have been encouraged by the squad that the club has put together and I believe Dai Young is building something really positive, and I hope that I can add to that.
"Hopefully I can see some game-time early on and push on from there."
London Wasps director of rugby Dai Young said: "Hugo is a great addition to the squad for the coming season, adding depth to the back three which is an area we identified as somewhere we needed strengthening.
"We've got a lot of young talent in our backline so bringing in someone with fantastic international and domestic experience will be a huge boost to the squad.
"He has a lot to offer and we look forward to seeing him in action."
Southwell becomes the 13th senior squad signing at Wasps for the new season, with Jeremy Castex (Narbonne), Steve Thompson (Leeds), Ross Filipo (Bayonne), Nicky Robinson (Gloucester), Ryan Davis (Exeter), Chris Bell (Sale), Chris Mayor (Gran Parma), Jonathan Poff (Crusaders), Simon McIntyre (Sale), Marco Wentzel (Leeds), Guillermo Roan (La Plata) and Alex Cheesman (Oxford University) already signed up.
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