The two clubs reached agreement over the transfer of the former Lecce and Juventus hitman for a fee thought to be in the region of £5.7 million. He will sign a four-year deal.
The 21-year-old will become Sven-Goran Eriksson's fifth signing since taking over at Eastlands, and the second Bulgaria international after compatriot Martin Petrov's arrival from Atletico Madrid.
"I'm very pleased that I'll have the chance to play alongside Martin [Petrov], as we did it in the national team," Bozhinov told gong.bg. "I've already talked to him several times.
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"I would like to thank manager Eriksson for making this move possible."
Bozhinov will undergo a medical later on Wednesday before being officially unveiled as a City player.
Bozhinov spent last season on loan with Juventus in Serie B, but a return to Florence was always unlikely after a dispute over pay soured his relationship with the Viola management.
The goal ace netted 16 times for Lecce between 2002 and 2004 but he failed to recreate that kind of form following a big-money move to Fiorentina, and was farmed out on loan to Juve last term.
Once in Turin, Bozhinov was rarely given the chance to play as the Old Lady won promotion back into the top flight and, after having realised he had become surplus to requirements at Fiorentina, he knew his time in Italy was up.
He added "I spent eight years in Italy and I think it's the right time to change country"."
Meanwhile, Croatia defender Vedran Corluka is nearing completing a move to Eastlands for a fee in the region of £8.7 million, according to reports in the Croatian press.
The 6ft 3in stopper - who would need a work permit to play in the Premiership - has become a priority for Eriksson after the Swede failed to land Italian Giorgio Chiellini.
Eriksson has already signed Italian striker Rolando Bianchi from Reggina, Brazilian midfielder Geovanni and Swiss Under-21 captain Gelson Fernandes.
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