The Blues ended Spurs' title challenge and Leicester were crowned Premier League champions following a 2-2 draw at Stamford Bridge which featured 12 yellow cards and two mass brawls involving players and coaches from both sides.
Matters came to a head again at the full-time whistle when a melee in the tunnel resulted in Chelsea's interim manager Guus Hiddink being pushed to the ground.
Both clubs were subsequently charged with three counts of failing to control their players, while Spurs midfielder Mousa Dembele was also handed a retrospective six-match ban for violent conduct after clawing his fingers down the face of Chelsea forward Diego Costa.
The clubs' sanctions have been reduced by £85,000 for Chelsea and £50,000 for Tottenham.
"An appeal board has reduced the fines issued to Chelsea and Tottenham Hotspur in relation to events at Stamford Bridge on May 2, 2016," a FA statement read.
"Following the game, both clubs were charged by the FA with failing to control their players and officials.
"An independent regulatory commission ordered that Chelsea be fined £375,000 and Tottenham Hotspur £225,000 after taking into consideration previous similar breaches of FA rules.
"However, following an appeal board hearing the fines have been reduced to £290,000 and £175,000 respectively
It remains that both clubs have been warned as to their future conduct."
Source : PA
Source: PA