The Blues have agreed that Silva, 39, can join his new team-mates prior to his registration transferring on 1 July.
The Brazil centre-back has signed a two-year contract with Fluminense.
He joined Chelsea on a free transfer from Paris St-Germain in 2020 and has made 152 appearances for the Blues.
Silva won three trophies in that time, including the 2020-21 Champions League.
He said his love for the club was “indescribable” in April, when he announced he would leave Stamford Bridge this summer.
Chelsea host Bournemouth in their final match of the season, with Mauricio Pochettino’s side seventh and fighting to finish in a European place with three league games remaining.
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