Gerard Pique says Barcelona are prepared to lose Xavi in the summer as reports link the midfielder with a move to Qatar.
After a season of uncertainty over the midfielder's future, the Blues have confirmed the England midfielder will remain at Stamford Bridge next season.
Lampard joined from West Ham in 2001 for £11million and has scored a club-record 203 goals in his 12 seasons in west London.
"I'm absolutely delighted," Lampard said in a statement on the official Chelsea website. "Everybody knows I always maintained the dream was to stay at Chelsea.
"We've been talking for ages and even though it went on for quite a period it was always amicable.
"I want to thank Mr Abramovich for everything he's done in making the dream a reality. I love this club, the staff, the players and especially the supporters, who have treated me fantastically since the day I arrived.
"The thought of helping the club to more success in the forthcoming years is all I ever wanted. I couldn't be happier."
Chelsea chief executive Ron Gourlay said: "Frank has been an important player for Chelsea Football Club for a long time and has played a significant part in the club's success.
"We have been talking to him since the end of last year and our discussions have been entirely positive throughout.
"We are delighted we are now announcing an extension to his contract which will keep him at the club until 2014."
Lampard is the third-highest appearance-maker in Chelsea's history with 607 appearances and next season will be his 13th at Stamford Bridge after joining from West Ham in 2001.
He recently surpassed Bobby Tambling's 202 goals for the club by scoring both goals in a 2-1 win at Aston Villa.
During his time at Chelsea, Lampard has won the Champions League, the Premier League title on three occasions, the FA Cup four times and the League Cup twice.
On Wednesday, he was part of the side that beat Benfica 2-1 in Amsterdam to win the Europa League.
Frank Lampard factfile:
1978: June 21 - Born, Romford, son of former West Ham defender Frank Lampard senior.
1995: Joins West Ham as a trainee.
October - Loaned out to Swansea.
1996: Makes his full debut as a second-half substitute against Sheffield Wednesday at Upton Park in May.
1997: August - Nets his first senior goal in the 2-1 win over Barnsley at Oakwell.
1999: October - Makes full debut for England when he starts in the 2-1 friendly win over Belgium at Sunderland.
2000: June - Captains the England Under-21s at the European Championship in Slovakia.
2001: May - Claims he wants to quit West Ham after boss Harry Redknapp and his father, assistant coach Frank senior, leave the club.
June 11 - Moves to Chelsea in an £11million transfer.
September 16 - Sent off for the first time in the Premier League after throwing a punch at Chris Perry in the 3-2 victory against Tottenham at White Hart Lane.
September 23 - Fined two weeks' wages after a Sunday newspaper publishes revelations of a drunken incident in a Heathrow hotel with team-mates Eidur Gudjohnsen, Jody Morris, John Terry and Leicester's former Chelsea defender Frank Sinclair.
2002: April 17 - Late substitute in England's 4-0 friendly win over Paraguay at Anfield but does not earn place in World Cup squad.
2004: June 24 - Scores extra-time equaliser in Euro 2004 quarter-final against Portugal but England lose on penalties.
September 19 - Sets new Premier League record for an outfield player of 114 consecutive appearances as he starts for Chelsea in their clash against Tottenham.
2005: April 28 - Voted Professional Footballers' Association Fans' Player of the Year.
April 30 - Scores twice against Bolton as Chelsea seal the Barclays Premiership title.
November 26 - Breaks record for consecutive appearances in the Premier League, making 160 appearances in a row.
November 28 - Second behind Barcelona's Ronaldinho as European footballer of the year.
December 19 - Second behind Ronaldinho as FIFA's world player of the Year.
December 28 - Run of consecutive Premier League matches ends at 164 as a virus rules him out of Chelsea's away match against Manchester City.
2006: April 29 - Wins back-to-back Premiership titles after a 3-0 victory over Manchester United at Stamford Bridge.
2007: February 25 - Wins Carling Cup with a 2-1 victory over Arsenal at the Millennium Stadium.
March 19 - Victim of an attempted attack on the pitch by a fan after Chelsea's 2-1 FA Cup quarter-final over Tottenham at White Hart Lane.
2008: March 12 - Scores four goals in Chelsea's 6-1 win over Derby.
April 24 - Mother Pat dies.
July 8 - Chelsea reveal they have rebuffed an approach for Lampard by Inter Milan.
August 13 - Signs a new five-year contract with Chelsea.
2009: January 17 - Captains Chelsea in his 400th appearance for the club with John Terry ruled out by a late injury.
May 30 - His 20th goal of the season is the winner in the FA Cup final, 2-1 over Everton.
September 9 - Scores twice as 5-1 win over Croatia secures England's place in the 2010 World Cup.
October 30 - Nominated for FIFA World Player of the Year award for sixth straight year.
2010: February 9 - Captains England in friendly against Denmark.
March 27 - Four goals in 7-1 rout of Aston Villa puts Lampard on 20 for a fifth straight season, and 151 for Chelsea, third all-time.
May 15 - Helps Chelsea retain FA Cup with 1-0 victory over Portsmouth in the final.
2011: September 2 - Left out of starting line-up against Bulgaria, the first competitive England match he did not start for four years when fit.
November 12 - Captains England and scores only goal in 1-0 win over world champions Spain.
2012: February 25 - Having struggled to hold down a place for Chelsea, publicly admits to problems with Portuguese manager Andre Villas-Boas.
April 9 - Scores his 150th Premier League goal in 1-1 draw with Fulham.
May 19 - Captains Chelsea to victory in the Champions League final. Chelsea win 4-3 on penalties, Lampard scoring, after a 1-1 draw.
May 31 - Ruled out of Euro 2012 with a thigh strain suffered in training.
2013: January 7: Lampard's agent Steve Kutner claims his client will not be offered a new Chelsea contract before his deal runs out in the summer.
March 17 - Scores his 200th Chelsea goal against former club West Ham.
May 11 - Breaks Bobby Tambling's Chelsea record of 202 goals as he scores twice at Aston Villa.
May 15 - Chelsea win the Europa League, beating Benfica 2-1 in Amsterdam.
May 16 - Signs a one-year extension to his Chelsea contract.