The highly rated youngster becomes Rangers’ seventh signing of the summer as Derek McInnes’ looks to strengthen his squad heading into the opening game of the season.
The 20-year-old joins the club on a deal worth to be approximately in the excess of £4 million.
Rangers have tied the youngster down to a four-year-deal with the option of an extra 12 months.
The Serbian was the captain of Partizan last season, aged only 19-years-old, and has already been called up to the national team.
The deal was almost certainly confirmed by McInnes last night after Rangers’ recent friendly match against Saint-Etienne.
McInnes said: “We are looking quite close to completing one or two things.
“I certainly think it’ll be at least two in for Sunday’s game and hopefully another one next week.”
This was after Dragojevic was spotted online with a Rangers cake decorated with the colours of the club earlier on in the week. He then addressed the cake situation after completing his move to the Glasgow club.
Speaking to Rangers TV, he said: “We made a dinner for my whole family because I was going to Rangers, and that was a surprise.
“I didn’t know. My friend made this, and everyone was there. It was a little emotional. Everyone was happy, but at the same time sad.”
Rangers have already added midfield firepower to their squad with the addition of Cammy Devlin and Dan Neil, making Dragojevic the third addition as Nico Raskin looks likely to depart before the end of the window.