The Guinea international has been swayed from AC Milan for €2.5 million, while the Paraguay forward has arrived for €5m from Benfica.
Constant arrives for a fee of 2.5 million euro from AC Milan, whom he joined from Genoa in the summer of 2012 before establishing himself as first-choice left back last season.
However, the Rossoneri, who are on the verge of signing Pablo Armero from Udinese, have now offloaded the Guinea international to Trabzonspor.
Constant, who can also play in midfield, is believed to have signed a four-year contract with the Super Lig outfit.
Trabzonspor also confirmed the capture of Cardozo from Benfica after agreeing to a €5m transfer fee with the Eagles.
The Paraguay international has also reportedly committed himself to the club until 2018.