The 18-year-old forward was omitted from Charlton's squad for their League One clash with Portsmouth on Monday night, which the Addicks won 2-1, to discuss a switch to Stamford Bridge.
Charlton owner Thomas Sandgaard had earlier told talkSPORT he had rejected two bids for the highly-rated teenager.
But Chelsea have now had an offer accepted, it is understood, and Burstow is bound for Stamford Bridge.
He is expected to remain at Charlton on loan for the remainder of the season before linking up with the Blues' development squad next season.
Charlton have a rich history of producing talented players through their academy and Burstow is the latest to have been tempted away.
Ademola Lookman, Ezri Konsa and Joe Gomez are three former Addics youngsters who have gone on to star in the Premier League.
Burstow is now set to follow them into the top-flight having impressed since making the step up to the Charlton first team, scoring 6 goals in 14 appearances.
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