The 28-year-old, who is part of England's World Cup squad in South Africa, has already been linked with Manchester United, Liverpool, Arsenal, Manchester City and Tottenham.
Related ArticlesL?Ballack will not be short of offersCole and Ballack to quit ChelseaJoe Cole leaves future until after World CupArsenal ahead in race to sign Joe ColeMichael Essien signs new Chelsea dealBranislav Ivanovic primed for South AfricaAs negotiations over a new contract at Stamford Bridge dragged on, it became increasingly likely Cole's seven-year stay would come to an end.
Manager Carlo Ancelotti had repeatedly stressed his desire to hang on to the midfielder but behind the scenes the parties could not reach an agreement.
Cole has been reluctant to discuss the situation in public but in March he confirmed talks had broken down, saying: "We can't seem to find common ground and it's distracting. At the moment there is no offer on the table, so I know where I stand."
Chelsea's stance is also likely to have been influenced by Cole's failure to hold down a regular starting spot this season.
The Londoner had been a key player in the rise of the club under owner Roman Abramovich but a serious knee injury suffered in Jan 2009 put him out for eight months and on his return he struggled to rediscover his best form.
Cole arrived at Stamford Bridge in a £6.6 million deal from West Ham in the summer of 2003 and helped Chelsea win their first Premier League titles under Jose Mourinho in 2005 and 2006.
Arguably Cole's best season for Chelsea came in 2007/08, when he picked up the club's Player of the Year award as they finished just behind Manchester United in the league and also lost the Champions League final to their rivals on penalties.
The last of Cole's 40 goals in nearly 300 appearances came in the 2-1 win over Manchester United in April that all but sealed a third Premier League triumph, while he also picked up three FA Cup winners' medals and two League Cup titles.
A move to another London club is likely to be appealing to Cole and Tottenham Hotspur manager Harry Redknapp confirmed he is interested in signing the midfielder.
Ballack leaves Chelsea after four years with the club unwilling to offer the German the two-year contract he was seeking.
The 33-year-old arrived at Stamford Bridge following the end of his contract at Bayern Munich with a reputation as one of Europe's best players and on the back of a brilliant World Cup.
But he has largely failed to live up to that billing, with injuries keeping him out of the team for lengthy spells.
Ballack helped Chelsea to their first Premier League title in four years this season while he also won the FA Cup three times.
But it was an ankle injury sustained in the last of those finals against Portsmouth in May that saw him ruled out of the World Cup, where he would have captained Germany.
Ballack will continue to be treated at Chelsea's Cobham training ground until his recovery is complete, when he is likely to receive offers from Germany while a move to join Jose Mourinho at Real Madrid has also been mooted.
Chelsea have also confirmed that right-back Belletti will be leaving the club when his contract expires at the end of this month.
The 33-year-old was signed by former manager Jose Mourinho in Aug 2007 and leaves after completing his three-year contract.