Fiorentina announced Valero's exit on Monday, with the Nerazzurri revealing the 32-year-old has agreed terms until 2020 at San Siro.
"Borja Valero Iglesias is officially an Inter player following the completion of all contractual formalities," Inter said in a statement on Tuesday. "The Spanish midfielder has penned a three-year deal with the club.
"Welcome to Inter, Borja!"
The move has been a controversial one, with Fiorentina having issued a statement threatening legal action against Valero over an audio message purported to be from the midfielder that was circulated on social media, which criticised the club.
Valero, who will wear the number 20 shirt, becomes new coach Luciano Spalletti's third signing following the arrivals of goalkeeper Daniele Padelli and defender Milan Skriniar.