The Bulgaria international has penned a four-year deal at the City of Manchester Stadium after passing a medical at City's Carrington training ground, although the deal is subject to a work permit.
The 21-year-old is Sven-Goran Eriksson's fourth signing in two days after deals for Javier Garrido, Vedran Corluka and Elano were completed on Thursday. He is Eriksson's eighth signing since being appointed City manager last month.
Bojinov was the youngest overseas player to play in Serie A when he made his Lecce debut aged just 15 years and 11 months after being plucked from Bulgaria a year earlier.
He scored 16 goals for Lecce and made his international debut against Italy at Euro 2004 in Portugal before joining Fiorentina in January 2005. The striker was loaned out to Juventus last season, where his goals aided the Turin giants' return to Serie A.
City chief excutive Alistair Mackintosh told the club's official website: "Our signing of Valeri is another sign of the impact made by (owner) Dr Thaksin Shinawatra) and Sven-Goran Eriksson. Valeri is an exciting young player and a great addition to the squad.''
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