Sidwell made 34 league appearances last season as the Seagulls returned to the top flight after a 34-year absence.
The 34-year-old joined Brighton on an initial loan deal from Stoke in January 2016, before joining the club on a free transfer ahead of last season.
"Steve has been a key member of the squad over the past 18 months," manager Chris Hughton said.
"Our fans know his qualities well, and his experience, particularly at Premier League level, will be important for us."

A total of 28% had not talked about the symptoms, the University of Aberdeen paper revealed.
Lead author Dr Peter Murchie said it highlighted the complications surrounding emergency cancer diagnosis.
Cancer Research UK said it was a complex area.
The study - published in the British Journal of Cancer - said that, of those who had previously flagged symptoms to their doctor, 81% had been appropriately referred on by their GP for further treatment or investigation of their symptoms.
However it said 19% could be viewed as missed opportunities for earlier diagnosis.
The study, funded by the Scottish Chief Scientist's Office, involved a review of the case notes from 1,800 patients diagnosed with cancer in northern Scotland and registered at GP surgeries across NHS Grampian, Orkney and Shetland.
Dr Murchie, a GP and researcher at the University of Aberdeen, said: "This study sheds light on the complications surrounding emergency cancer diagnosis and how quickly circumstances can change for the patient.
"It's vital we do more to ensure people with persistent or unusual symptoms feel confident about getting them checked out by a doctor without delay.
"And it's equally important to give GPs better access to the tests and specialist advice they need to help them spot potential cancer symptoms at the earliest stage."
Jodie Moffat, Cancer Research UK's head of early diagnosis, said: "For some patients, emergency presentation may be difficult to avoid, but for others there are often things that could have been done differently.
"Studies like this help us to understand this complex picture and identify what needs to change.
"Cancer patients diagnosed as an emergency are more likely to have late stage disease and poorer survival. So it's vital we do all we can to break down barriers to people visiting their doctor with symptoms that could be cancer.
"Cancer Research UK is also working with GPs in Scotland to help improve early cancer diagnosis and ensure they have the freedom to refer patients for further tests and access specialist advice if cancer is suspected."

Cardiff Metropolitan University wants to create the seven-storey facility at Queenswood - part of its Cyncoed campus.
Residents and the Woodland Trust said it would affect species including bats, birds and foxes.
The university said it had done environmental impact studies.
On Cardiff council's website, the application is listed with 133 objections, mainly from Cyncoed residents and councillors, and three petitions against it.
A spokeswoman for Cardiff Metropolitan University said it was decided to build the new accommodation as demand from students to live on-site outstrips supply.
Its plans for the 518-bed facility is on a third draft, with its position moved four times to protect the woodland, part of the campus since the original college was established in 1962.
However, the Woodland Trust has objected to Cardiff council about "damage and loss" of the "irreplaceable habitat".
The body's Heini Evans said: "Ancient woodlands support a huge array of wildlife and we need to protect these special areas."
An ancient woodland is an area that has existed continuously since 1600 or before, with these supporting more than 256 species.
But only 2% of the UK's land area is covered by them.
Resident Neil Gardner said Queenswood has mature oak trees, bluebells, protected bats, hedgehogs, foxes and many species of birds.
"As the wood is destroyed all these will be lost to the community with a considerable environmental impact on local residents," he said.
"This is an ecological and environmental crime and is intolerable to local residents."
The university spokeswoman added: "There has been lots of work to negate possible impact on wildlife including biodiversity and environmental studies.
"The university has also completed the various 'in season' studies which have been forwarded to the planning authority."
A public consultation period ended last week and council planners will meet to discuss the proposal at a later date.
Brighton midfielder Steve Sidwell has signed a new one-year contract with the newly-promoted Premier League club.
[NEXT_CONCEPT]
More than a quarter of cancer patients diagnosed as an emergency in the north of Scotland had not discussed any relevant symptoms with their GP beforehand, according to a new study.
[NEXT_CONCEPT]
Plans to build student flats on ancient woodland have been described as "an environmental crime" by campaigners opposed to the move.