Fernando Torres will join Milan permanently on January 5 ahead of his expected return to Atletico Madrid.
Liverpool boss Brendan Rodgers has insisted Mario Balotelli will not be going out on loan in the January transfer window.
The 49-year-old takes over from Attilio Perotti, who only replaced sacked Davide Nicola on January 13.
A statement from Livorno read: "Livorno announces that this (Tuesday) afternoon, the new coach of the Amaranto's first team Domenico Di Carlo will be unveiled to the media."
Livorno lost 3-0 at Roma on Saturday in what was Perotti's first game in charge.
The sacking of Nicola and the appointment of Perotti as his replacement had not been welcomed by the club fans.
Saturday's loss was Livorno's fifth consecutive defeat and dropped the Tuscan outfit to 19th place, with 13 points from 20 games.
Di Carlo, who played one season at Livorno, last coached in Serie A when he guided Chievo in the 2011-12 campaign.
His first game in charge will be at home to Sassuolo on Sunday.
Perotti, meanwhile, is expected to return to his role as technical director of the club, a position he held prior to being named as Nicola's successor.