The forward struck twice on debut in victory against Livorno in midweek.
"I am very happy to be at Lazio. I would like to once again thank the club as they had a lot of faith in me," Floccari said.
"I would like to thank Genoa who have given me this great chance. I soon made a wonderful impact. I arrived on Tuesday and went on the pitch on Wednesday, and for this I would like to thank Davide Ballardini and my team-mates who made me feel very welcome.
"It had been a difficult few months for me in Genoa. Now I have a lot of desire to re-make myself. There are the conditions for us all to do well. I have found a compact group of players with a lot of enthusiasm.
"There is a lot of work to do, because Lazio don't deserve to be where they are in the table. My decision has been put into perspective."