Chelsea's outlay reflects their transfer market activity following the return of Jose Mourinho as manager.
Manchester City, who had spent more on fees than anyone else for the previous two years, spent £11m.
Champions Manchester United spent £4m despite struggling to add to their squad in the summer transfer window.
In total, clubs paid £19m more than last year to agents following the increase in revenue from the new television deal and averaged more than £4.5 million each.
Crystal Palace were the only club to spend less than a million on fees, paying £869,532 to agents.
Chelsea recruited Andre Schurrle, Willian and Samuel Eto'o during the close season to help their title challenge, while the arrival of Manuel Pellegrini as Manchester City manager prompted the recruitment of Jesus Navas, Stevan Jovetic and Alvaro Negredo.
Tottenham paid a £9m in agents fees having spent heavily to expand their squad following Gareth Bale's record-breaking transfer to Real Madrid, bringing in players like Roberto Soldado, Christian Eriksen and Erik Lamela.
By contrast, Manchester United made only one major signing following the retirement of Sir Alex Ferguson, with Marouane Fellaini joining from Everton on deadline day.
Southampton, one of the surprise packages of the season, spent £2m on fees.
Total money spent on agents (Oct 2012-Sep 2013)
Source: Premier League
West Ham United
West Bromwich Albion