City have signed Spanish defender Javier Garrido, Croatia center-half Vedran Corluka and Brazilian midfielder Elano, who was a part of the team that clinched Copa America last month.
The 21-year old Bojinov has penned a 4-year deal for an undisclosed fee, signing from Serie A side Fiorentina.
The promising Bulgaria striker spent last season on-loan at Juventus, but manager Claudio Ranieri was not convinced to offer him an extension.
City are also on the verge of completing a move for Australia midfielder Mark Bresciano from Palermo.
Former England manager Eriksson said he will not cut spending until he achieves a certain target for the new-look City squad.
"My dream is to have eight defenders, eight midfielders and four strikers. That is what I am working towards and hopefully, by the time I have finished, that is what I will have," Eriksson stated in a press conference.