The 21-year-old was close to joining Portsmouth earlier in pre-season, but the deal collapsed and Rovers boss Sam Allardyce has swooped.
Allardyce, who has spent the summer searching for forwards, has previously confirmed his interest in Kalinic and he now appears to have got his man.
The Hajduk Split star's representative, Tomislav Erceg, claims a deal has been agreed between the clubs and all that is now required is to obtain a work permit.
"It is finished, the transfer is completed. Now all Nikola needs is a work permit, which shouldn't be problem," Erceg told Sportske novosti.
Kalinic said: "I can at last focus on football.
"I want to begin training with my new team as soon as possible and get into top form."
Reports say Kalinic has signed a four-year deal with Rovers, where he will be expected to replace Roque Santa Cruz following his move to Manchester City.
Rovers have also brought in Franco Di Santo on loan from Chelsea to give Allardyce's attacking options a further boost.