Malouda and his former Chelsea team-mate, Bosingwa, who also played for Queens Park Rangers, have been pictured undergoing medicals and will arrive as free agents.
France international Malouda was released by Chelsea at the end of last season after spending the whole of the 2012/13 campaign frozen out of the first team.
Bosingwa, who spent four years at Chelsea between 2008 and 2012, joins from QPR, who earlier on Sunday announced the former Portugal defender had left the club by mutual consent.
Trabzonspor said in a statement on their official website: "Florent Malouda and Jose Bosingwa signings tomorrow (Monday) at 21.30 at Huseyin Avni Aker Stadium. All fans are invited."