Surman, who joined from Wolves two summers ago, scored five goals last season as City enjoyed a successful return to the Premier League.
And the midfielder is looking forward to life under a new manager following Paul Lambert's departure and the arrival of Chris Hughton.
He said: "It feels great. I've really enjoyed my time here and I'm looking forward to another three years.
"We've a new manager coming in now, and it's a great time to build on what we did last season. Everything I've heard about the new manager is really good."
Hughton said: "Andrew did really well for Norwich last season and as manager I am pleased that he has accepted our offer."
Borussia Dortmund hears Wembley Calling and are headed to London for the Champions League final.
The new PUMA evoSPEED 1.2 FG. A great new soccer cleat with classic look and first time for PUMA to be on the cleat.
Chelsea won the Europa League on Wednesday. The Blues defeated Benfica 2-1 on injury time goal from Ivanovic.
The push for more color on their cleats, adidas has added the infrared colorway to the adiZero f50 Line.
One of the top soccer cleats for control the Nike CTR360 will not let you down on the field in tight spaces.
adidas has added some color to the Predator line with this new colorway. Released on May 17. Be the first to own a pair.
The Liverpool 2013/14 soccer jersey is available for pre-order. The Reds are eager to compete for silver next season.
The adidas Nitrocharge is the most talked about new cleat in years. It was released on May 15 and will take your pitch by storm.
Ajax has released their away soccer jersey for the 2013/14 season. Get in the Gear.
The Juventus jersey for the 2013/14 was released earlier this week. Be the first to wear the colors of the Old Lady.