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.
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.