The 24-year-old had looked set for a move to Burnley, with the two sides in contact about a deal.
But a Forest statement said: "The 24-year-old has declared his intention to stay following a conversation with (chairman) Fawaz Al Hasawi.
"The club welcome Lansbury's decision and will now move forward with him in their plans."
Lansbury, who had loan spells with Scunthorpe, Watford, Norwich and West Ham when an Arsenal player, is currently the Reds captain.
Al Hasawi tweeted a picture of himself and the player, saying: "Henri is staying with us."

About 80 items, including artwork, letters and clothing from collections around the world will go on display in Winchester in the summer.
Exhibits will include the author's silk pelisse coat, her purse and sewing box.
A portrait, not been seen in public for more than 40 years, is also included.
It is one of five to be brought together for the show.
The exhibition takes place at The Gallery in Winchester Discovery Centre - a few miles from Austen's birthplace of Steventon - from 13 May to 24 July.
Co-curator Louise West said: "The bringing together for the first time of five portraits of Jane Austen will, we hope, provoke reaction and excite argument about the mysterious Miss Austen.
"This is a new way of exploring Austen's identity and we are thrilled to be sharing this opportunity with the public."

The USA had taken a one-point lead into the final day at Nairn with the scores at 6.5-5.5.
However, the home players won the final day's play by 5-3, with Northern Ireland's Stephanie Meadow scoring the crucial point as she beat Amy Anderson.
It means Europe or Great Britain and Ireland hold all the major trophies they compete for against the USA.
The Curtis Cup joins the Ryder, Solheim and Walker Cups on this side of the Atlantic for the first time in golf history.
Britain and Ireland 10.5 - 9.5 United States
Singles
Kelly Tidy (B&I) def. Austin Ernst (US) 2&1
Amy Boulden (B&I) def. Emily Tubert (US) 3&1
Holly Clyburn (B&I) def. Erica Popson (US) 3&2
Lisa McCloskey (US) def. Pamela Pretswell (B&I) 4&3
Tiffany Lua (US) def. Bronte Law (B&I) 2 up
Charley Hull (B&I) def. Lindy Duncan (US) 5&3
Stephanie Meadow (B&I) def. Amy Anderson (US) 4&2
Brooke Pancake (US) def. Leona Maguire (B&I) 6&5
Nottingham Forest have confirmed that midfielder Henri Lansbury will stay with the Championship club.
[NEXT_CONCEPT]
An exhibition marking the 200th anniversary of Jane Austen's death will feature writings from her teenage years and the original ending she wrote for her novel Persuasion.
[NEXT_CONCEPT]
Great Britain and Ireland ended a 16-year wait for Curtis Cup glory by beating the United States.