Del Neri, 62, immediately faced questions about his past at bitter rivals Sampdoria as he took his place in the hot seat for his first coaching job since he was sacked by Juventus at the end of the 2010/11 season.
"You can't cancel the past," Del Neri, who has coached more than 15 teams including Roma, Porto and Atalanta, told reporters.
"The season at Sampdoria was important one in my career," added Del Neri, who coached Sampdoria in 2009/10.
"Genoa is one of the most important footballing cities of Italy, it demands a lot of you but also gives great incentives because of the desire for football."
Since Gian Piero Gasperini left in November 2010, Genoa have employed Davide Ballardini, Alberto Malesani twice, Pasquale Marino and De Canio as coach.
Malesani's second stint in April lasted less than one month and ended a day after a 4-1 home defeat against Siena, a match interrupted for 45 minutes as fans protested and demanded that Genoa players take their shirts off.
De Canio replaced him and was fired on Monday, one day after Genoa, tenth with nine points from eight games, squandered a two-goal lead and lost 4-2 at home to AS Roma.
Palermo, Chievo and Pescara have also changed coaches in the first eight rounds of matches.