Wisdom, 23, had been heavily linked with a reunion with his former Liverpool manager Brendan Rodgers at Celtic, but the Austrian side have now completed the deal.
Liverpool have also sold Spanish forward Luis Alberto to Serie A side Lazio for £4.3m.
And midfielder Lazar Markovic has joined Sporting Lisbon on loan.
Alberto, 23, made 12 appearances for Liverpool after he was signed by former manager Brendan Rodgers from Sevilla in a £6.8m deal in June 2013.
He impressed while on loan at Spanish side Deportivo La Coruna last season, scoring six goals.
The fee also includes add-ons and a 30% sell-on clause for the Reds.
Markovic, who joined Liverpool from Benfica for £20m in July 2014, has struggled for opportunities at Anfield and spent last season on loan at Fenerbahce.
Sporting wanted to sign the 22-year-old Serb on a permanent deal earlier this summer but he had no desire to return to Portugal.
However, he has now had a change of heart and will stay with the Primeira Liga club until the end of the season.
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Liverpool defender Andre Wisdom has joined Red Bull Salzburg on a season-long loan deal.