The Ivory Coast international, 27, said he wanted to leave in August and was a target for Everton.
However, a move did not materialise for Kone, signed from French Ligue 1 club Lorient in January.
"Lamine is an important player for this club and I made that clear to him from the outset," said Sunderland manager David Moyes.
Kone was signed by Moyes' predecessor Sam Allardyce and played a key role in their survival in the top flight last season.
Moyes added: "He only been playing in the Premier League since January, but in that time we have already seen what he is capable of.
"The challenge for Lamine now is to build on what has been a very positive introduction to English football and to continue to improve and grow as a player."

Graham Stringer and Andrew Miller fear standards have slipped since the Forensic Science Service shut in 2012.
Much of the work is now done by in-house police laboratories, many of which have not been accredited to a recognised international standard.
The Home Office said: "We continue to ensure forces have access to the best possible forensic services."
Figures obtained through Freedom of Information requests by The Sunday Post show North West police forces have cut their forensic science budgets by nearly £10m over the past five years.
Greater Manchester Police has seen the biggest reduction, down from £18.7m in 2010-11 to £13.8m in 2013-14.
Budget projections from Greater Manchester's Police and Crime Commissioner Tony Lloyd reveal plans to cut a further £1.6m by 2017.
Lancashire Constabulary, meanwhile, has cut its forensic science budget from £3.3m in 2010-11 to about £990,000 in 2013-14.
Mr Stringer, Labour MP for Blackley and Broughton, claimed "murderers and rapists are likely to go free" because of the cuts.
He said it was "good news for criminals" and has made "a very bad situation worse".
Mr Stringer said the range of forensics services now available through police laboratories and the private sector were limited and it was a "really worryingly situation".
Ellesmere Port and Neston MP Mr Miller said: "There's a real fear that somebody is going to end up on the wrong side of the bars, either someone wrongly prosecuted or wrongly acquitted, because of this cost-cutting approach that has been adopted."
The Labour MP said there was a lack of transparency on how money was spent, and added: "There is a real risk that in-house police laboratories will undermine the integrity of the whole industry of forensic science."
Six of the forensic science services undertaken by GMP and seven of those performed by Cheshire Constabulary do not have accreditation from the International Standards Organisation.
In December, a National Audit Office report raised doubts about the effectiveness of Home Office oversight, pointing to what it described as a lack of data on forensics spending by police forces.
The Home Office said police reform was working and that "it is for police and crime commissioners and chief constables to decide how to spend their budgets".
December 2010: The government announces plans to close the Forensic Science Service (FSS), a government-owned company which employs 1,600 staff. The government says it is losing about £2m a month
July 2011: An MPs' inquiry concludes that the government did not consider the wider impacts of closing the FSS, and that financial reasons took precedence
October 2011: In its official response to the inquiry, the government argues that allowing the FSS to enter administration would have caused serious damage to the criminal justice system
March 2012: The FSS officially shuts its doors, with operations transferred to private companies and in-house police laboratories.
July 2013: A follow-up inquiry by the Commons' Science and Technology Committee concludes that major crimes could go unsolved unless the government does more to support forensic science
November 2013: The government launches a consultation over plans to boost the powers of the forensics regulator in England and Wales
Sunderland defender Lamine Kone has signed a new five-year contract with the Premier League club.
[NEXT_CONCEPT]
Cuts in forensic science spending risk serious mistakes being made in criminal cases, two North West MPs have warned.