The 30-year-old Serb said he had agreed to surgery after last month's Australian Open when he was treated on court in losing to unseeded South Korean Chung Hyeon in the last 16.
"I agreed with my team that I would try different methods after I finish in Australia and a few days ago I accepted to do a small medical intervention on my elbow. It seems like I am on the good road now to full recovery," he posted on Instagram.
The 12-time grand slam champion had hoped the extended break he took last year might solve the problem but said he decided on more drastic action after still experiencing pain in Melbourne.
"I've been carrying this injury for the past two years, and during this time I've been seeing many doctors," said Djokovic, who before last month had not competed since losing at Wimbledon last year.
"I took six months off last season hoping to come back fully recovered, but unfortunately I still felt pain," he said.
"It's quite a journey this one, I have to say. I'm learning a lot and for that I'm grateful. I've always taken care of my body and looked for the most natural ways to heal, and my body has rewarded me with some incredible years on tour.
"I am super positive and excited to follow my recovery through so I can come back to the place I love the most. The court."
Serbia's former Davis Cup coach Bogdan Obradovic predicted Djokovic would make a full recovery.
"I am convinced that Djokovic can return stronger, he has overcome many problems in his career," said Obradovic, who led Serbia to their maiden title in the competition in 2010.
"He has made all the right moves - he took a break in an effort to avoid surgery, played at the Australian Open and when it didn't work, having the surgery was the only option.
"He is still hungry for success and what he needs to do now is be patient," he told Reuters.
Djokovic's rival, Britain's Andy Murray, is also recovering from surgery, to his hip, after also finding that rest did not cure his long-term injury.
(Reporting by Neil Robinson; Additional reporting by Zoran Milosavljevic in Nis, Serbia; Editing by Ken Ferris)
