The 23-year-old moves to the Britannia Stadium on a four-year contract for an initial fee of £3.5m, which could rise to £5m.
Potters manager Tony Pulis said: "Steven is an outstanding young prospect.
"He has made a big impact in the Premier League since he arrived at Blackburn three years ago and I am sure he will prove to be an excellent addition to our squad.
"He is the type of player who will endear himself to our supporters."
N'Zonzi, who was capped six times by France at Under-21 level, made 86 Premier League appearances during three full seasons at Ewood Park.