Subotic's current deal is due to expire in June 2014, and the Serbia international was linked with a move away from BVB on more than one occasion.
Nevertheless, the 24-year-old has now ended speculation over his future, and will sign a two-year extension on Monday.
"Neven and BVB have reached an agreement. He will sign an extension until June 2016 with Dortmund. He's feeling very well at BVB and in this city," Kelly told Der Westen.
Subotic could face a three-week spell on the sidelines after picking up a calf injury at Dortmund's training camp in La Manga, Spain.
The defender will undergo further examinations on Tuesday.
Meanwhile, Dortmund has also agreed terms with midfielder Sven Bender over a contract extension until the summer of 2017.
"We are delighted that both players will remain at Dortmund for a long time," sporting director Michael Zorc commented.