The Italian joined in October after Forest made a British record 22 signings in the summer, overseeing their January transfer window spending.
Forest, who have won only once since January, said Giraldi has left “amicably”.
Last week owner Evangelos Marinakis said results “must improve immediately” under manager Steve Cooper.
Forest dropped into the Premier League relegation zone on Saturday as a 2-0 defeat at Aston Villa extended their winless run to nine games.
In January they signed Brazilian midfielder Danilo from Palmeiras for about £16m, midfielder Jonjo Shelvey and defender Felipe for undisclosed fees, midfielder Gustavo Scarpa on a free transfer, plus striker Chris Wood and goalkeeper Keylor Navas on loan.
Source – BBC Sport
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