Thioune, who became the first German-born black head coach when he took over at Osnabruck in 2017, joins on a contract until 2022.
His appointment comes after Hamburg parted ways with Dieter Hecking following their failure to secure a return to the Bundesliga.
A 5-1 home defeat to Sandhausen on the final day of the season denied Hamburg a place in the promotion play-off and condemned them to a third campaign in the 2. Bundesliga.
Thioune guided Osnabruck to promotion from the 3. Liga in 2018-19 and then a 13th-placed finish in the second tier as they avoided relegation.
He said: "For me, the task at hand at HSV will be a great challenge, which I would like to tackle head on with diligence, team work and passion.
"Everyone knows that HSV wants to be back in the Bundesliga. But to talk about that, doesn't bring us closer to that goal.