Jankto, 22, made 36 Serie A appearances for the Zebrette last season, scoring four goals from deep.
The Czech Republic international was in Genoa earlier on Friday for his medical, and the club announced on social media that they had completed his transfer.
Jankto had previously been linked with Arsenal, but it now seems he will act as the replacement for Torreira, who is a reported target for Unai Emery in North London.
The Uruguay international midfielder has been linked with the Gunners for some time and a deal appears close.
Torreira’s father told Teledoce recently: “It’s a big change [going to England] and we don’t want to think about it yet because we’re scared.
“The truth is it’s tough to manage the language, adapt to the [London] society and customs and at the same time not lose ours.
“But there’s a whole programme getting readied for Lucas.”