Top goalscorer Mbappe had been sidelined for two weeks, but Real said the French striker completed part of the group session two days before their trip to Barcelona.
Tchouameni also took part in training the day after his altercation with Valverde resulted in the latter reportedly needing stitches.
The team confirmed that disciplinary proceedings have been opened against both players after the training ground clash, one of a spate of such incidents.
Tensions are high at Real with the prospect of a second consecutive season without a major trophy.
Leading by 11 points, Barcelona only need a draw in the Clasico to be crowned Spanish champions again.