The Football Association has fined Chelsea and Tottenham £375,000 and £225,000 respectively for failing to control their players during the 2-2 Premier League draw at Stamford Bridge on May 2.
Both clubs have admitted three breaches of FA rule E20 in relation to incidents in the 45th and 87th minutes of a heated London derby.
That incident was missed by the match officials but captured by television cameras, with Dembele subsequently hit with a six-match ban.
Chelsea came from two goals down to ensure a share of the spoils, with Eden Hazard's 83rd minute equaliser confirming Leicester City as Premier League champions at Tottenham's expense.
In a statement confirming the punishment, the FA referenced four separate breaches by Chelsea under rule E20 since November 2014, alongside two offences from Tottenham during the same period.
