Gasperini led the Rossoblu to promotion from Serie B in 2007 and enjoyed mixed fortunes across three seasons in the top flight before being sacked in November 2010.
But Genoa president Enrico Preziosi has restored the 55-year-old to the Marassi hotseat after promoted youth coach Liverani oversaw four defeats and only one win from six games, culminating in Saturday night's 2-0 home loss to Napoli.
A statement published on Genoa's official website read: "Genoa has entrusted the care of the first team to Gian Piero Gasperini. The agreement reached covers the next three years.
"The club thanks Fabio Liverani for the work he did and for his dedication to the cause over recent months."
The summer promotion of former Lazio midfielder Liverani from his role with youth team was seen as a progressive move for Preziosi, who has typically preferred experienced coaches since purchasing the club in 2003.
It was, however, an inauspicious start for the 37-year-old as back-to-back Serie A defeats to Inter Milan and Fiorentina followed a shock exit to Spezia in the Coppa Italia before he redeemed himself by delivering a 3-0 derby victory over Sampdoria.
But a goalless draw with Livorno was followed by defeats to Udinese and Napoli in which the Grifone also failed to score, prompting a managerial switch - the first of the new Serie A season.
Gasperini returns to Liguria after brief stints at Inter Milan and Palermo - with whom he spent two separate spells last season - and the appointment is likely to divide opinion among the club's fanbase.
In 2009 he led Genoa to fifth place and the Europa League with some enterprising football and oversaw a third consecutive derby win over Sampdoria later that year.
However, the start of the 2010-11 season yielded only 11 points from 10 games despite the presence of star signings Luca Toni and Miguel Veloso and, with relations suddenly souring between the pair, Preziosi sacked Gasperini on November 8.