File Photo: Then-Roma's head coach Daniele De Rossi. AP
Genoa said in a brief statement that it was "extending a warm welcome to Daniele De Rossi", who was to lead an afternoon training session.
He will hold his first press conference on Friday.
Genoa were winless in Serie A when Vieira agreed to leave on Saturday morning, but Roberto Murgita and under-17 coach Domenico Criscito led the club to a 2-1 win at Sassuolo on Monday night that lifted them off the bottom of the table.
Rossi, a rugged midfielder who won the World Cup with Italy in 2006, played 17 seasons for his home-town club Roma and won 117 Italy caps.
He had brief stints as a coach at second-vision Spal, where he lasted 17 games in 2022 and then 30 at Roma.
He took Roma to the 2024 Europa League semi-final but was fired after four winless games at the start of the following season.
Last week, Genoa also sacked sporting director Marco Ottolini and have replaced him with Spaniard Diego Lopez.
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