PIatek, who has joined on loan from Hertha Berlin for the rest of the season with an option to buy, returns to Serie A after previous spells at Genoa and AC Milan.
The 26-year-old has a solid track record in the Italian top flight, and his arrival has inevitably added to speculation that Vlahovic may not be with Fiorentina for much longer.
Vlahovic's record of 35 goals in 46 games in 2021 has drawn the attention of many of Europe's elite teams, and he has also been linked to Newcastle United.
It has been reported in Italy that Fiorentina consider Piatek as a player to strengthen its squad, rather than as a replacement for 21-year-old Vlahovic.
Polish frontman Piatek is relishing the chance to play alongside the young Serbian when the chance arises, saying: "Vlahovic is an excellent striker, he has scored many goals.
"I think I also showed my worth with Genoa and Milan. I think we can also play together when necessary. In any case, I'm at the coach's disposal, even starting from the bench."
Fiorentina sits sixth in Serie A heading into Monday's (AEDT) trip to Torino, with coach Vincenzo Italiano hoping Piatek can rediscover the form that saw him score 30 goals in the 2018-2019 season.
He began that campaign at Genoa before heading to AC Milan in mid-season, typically marking his goals with finger pistol celebrations.
"I'm ready to be a gunslinger. I want to show that my guns are ready to shoot at the Franchi. I'm really very happy to be here," Piatek added
Fiorentina has also signed forward Jonathan Ikone from Lille for a reported €15 million ($23.6 million) fee this month, so it would be well stocked if Vlahovic did move on.
There seems little prospect of Isco joining the Viola ranks, however, with sporting director Daniele Prade distancing the club from reports linking them to the 29-year-old.
Isco has been at Madrid since 2013, making more than 300 appearances for Los Blancos, but he has become a fringe member of Carlo Ancelotti's squad, leading to rumours of a move.
Prade said: "In recent days there have been many rumours about Isco, but we don't even know the agents, so we are not interested, even though we recognise his value."