The League One club appointed Milanese as manager in October when he replaced Russell Slade, but have taken just four points since the Italian took over and also bowed out of the FA Cup.
Saturday's 1-0 defeat to Gillingham proved the final game in charge for the former Italy international with countryman Liverani taking over alongside Marcello Donatelli and Maurizio Cantarelli as assistant and fitness coach respectively.
Liverani - also a former Italy international - has managerial experience from his time at Serie A side Genoa and will take training from Tuesday.
"I'm excited about this challenge and cannot wait to get started at Leyton Orient," he told the club's official website.
"This is a long term project and we will work together to make it a success."
Liverani's first game in charge will be Saturday's league clash with Peterborough United at Brisbane Road.
For Orient, the reshuffle is the latest in a series of backroom changes this season following the club's near-miss in gaining promotion to the Championship last term.
Kevin Nugent initially took over as interim boss following Slade's departure before Milanese assumed control, with Liverani arriving on a two-year deal.
