Adam, 26, who joined the Reds in a £9m move from Blackpool in July 2011, is thought to have cost £4m.
The Scotland international, who has also played for Rangers, has signed a four-year deal.
Frenchman Nzonzi, 23, also signed a four-year deal for an initial £3.5m that could eventually rise to £5m.
He had not featured for Blackburn this season after making it clear he wanted to leave the club following their relegation.
Nzonzi joined Rovers from French side Amiens in 2009 and made 97 appearances for the Ewood Park club, scoring three goals.
Stoke manager Tony Pulis believes the addition of Adam will make a significant improvement to his team's attacking options.
He said: "It's no secret that we've been looking to bring more goals to the squad and Charlie is a fantastic signing in that respect.
"Not only will his creativity and his eye for delivering a pass be a great asset to us, he scored 12 goals for Blackpool in the Premier League two seasons ago."
Adam added: "This club's on the up and it's great to be a part of it. I can do this club proud and I'm looking forward to the chance of playing in front of their passionate supporters."
Stoke have signed Liverpool midfielder Charlie Adam and Blackburn's French youngster Steven Nzonzi.