The talented Bulgarian becomes City’s fourt signing in two days.
Bojinov spent last season on-loan at Juventus.
Bojinov will sign a four-year deal, subject to a work permit.
City chief executive Alistair Mackintosh told the club’s official website: “Our signing of Valeri is another sign of the impact made by Dr Thaksin and Sven-Goran Eriksson.
“Valeri is an exciting young player and a great addition to the squad.”