The London team has only once before turned a profit in the 10 years since it was acquired by Russian billionaire Roman Abramovich.
The club said a new TV broadcasting deal, as well as the sale of players such as Juan Mata, had boosted profits.
Chelsea are currently unbeaten at the top of the Premier League.
They also top their Champions League group.
In 2012, Chelsea reported a profit of £1.4m, its first under Mr Abramovich. The club then made a loss in 2013.
This year's profits mean the club satisfies the Financial Fair Play (FFP) rules imposed by Uefa, European football's governing body.
Under FFP, clubs need to balance football-related expenditure - transfers and wages - with television and ticket income, plus revenues raised by their commercial departments.
Money spent on stadiums, training facilities, youth development or community projects is exempt.
Bruce Buck, Chelsea's chairman, said the club's focus was first and foremost on the team's performance.
"By reaching the Champions League semi-final and maintaining a challenge in the Premier League until the final week of the season we demonstrated that, while improving our financial figures, we remained competitive in football's toughest club competitions," he said.

Stuart Hyde, ex-chief constable of Cumbria Police, was put into a medically-induced coma and treated for the viral infection.
Mike Pannett, co-director of the 4 Policing consultancy with Mr Hyde, said he was now out of the coma and talking.
He said his family thanked everyone for the messages of love and support which had helped them all "so much".
Mr Hyde retired in 2013 after being suspended twice from the force, investigated and cleared.

The 41-year-old replaces former Scotland team-mate Graham Alexander, who was dismissed on 30 September.
Pressley was sacked by Coventry City in February after almost two years in charge, following a seven-game winless run that left them in the relegation zone.
He recently rejected the chance to talk to Scottish side Dundee United about their vacant managerial position.
Pressley has been working as a coaching for the Scottish Football Association and had just agreed to look after the Scotland Under-17 team on a one-off basis for a three-match round of qualifiers.
In a recent interview with BBC Radio Scotland, after being linked to the role at Dundee United, Pressley said: "I have built up a very good reputation in England and I have a burning desire to manage at the elite level.
"That's not an arrogance. That's a belief. In order to do that, I think you have to manage in a country like England."
The former Hearts and Rangers centre-back started his coaching career at Falkirk in 2010, leaving the Bairns three years later to take charge of Coventry.
He kept the Sky Blues in League One in his first full season in charge despite serious financial difficulties which resulted in the club being docked 10 points for going into administration.
He was fired the following year with Coventry 21st in the table, in a season when they were beaten at home in the first round of the FA Cup by non-league Worcester City.
Meanwhile, Fleetwood have confirmed that assistant manager Chris Lucketti will remain in his role, while Pressley's former Coventry assistant Neil MacFarlane has joined the coaching staff.
Chelsea Football Club has reported a record profit of £18.4m ($29m) for the year to June 2014 - despite last season's lack of silverware.
[NEXT_CONCEPT]
A former top British police officer is out of a coma after contracting meningitis while working in Abu Dhabi.
[NEXT_CONCEPT]
League One side Fleetwood Town have appointed Steven Pressley as manager.