Rovers boss Mark Hughes is delighted to win the race for Santa Cruz, who was at Ewood Park last night for a medical.
Hughes said: "We have some very good strikers at this club, but what we haven't got is a real aerial threat, and that's where Santa Cruz can help.
"He's a 25-year-old international from Bayern Munich, and to get that quality through the door in comparison to other deals that have been done would be exceptional.
"Santa Cruz has been at Bayern for a number of seasons but his progress has been hampered by injuries. Just as he was getting a place in the side he was getting injured, so it was stop-start which was frustrating for him. But you don't stay at a club like Bayern for as long as he has without having great ability."