The 12-time Grand Slam champion split from Andre Agassi and Radek Stepanek earlier this month and has been training with Vajda for the last 10 days in Monaco.
"It's a fresh start I think for both of us. I missed him. I have a feeling that he missed me or tennis or both," Djokovic said after a confident 6-0, 6-1 thrashing of Dusan Lajovic in the first round.
"He knows me better than any tennis coach I've worked with.
"He's a friend. He's someone I can share a lot of things with, whether it's professional or private life. He's always there for me."
Djokovic confirmed he is not yet working with Vajda on a full-time basis, after the two parted ways following last year's tournament in Monte Carlo.
The 30-year-old also played down reports of a rift between him and Agassi, thanking the American for "helping his career" over an 11-month period.
"This doesn't affect our personal relationships that we established over the years both with Radek and Andre," he said.
"But we just decided that it's better to part ways because, you know, both sides did feel that that's best for me and for them."
Monday's win was his first since the Australian Open in January, after being dumped out in Indian Wells and Miami by Taro Daniel and Benoit Paire respectively.
The Serb said he is now playing pain-free, after struggling with a right elbow injury.
"After two years, finally I can play without pain," added Djokovic.
"Indian Wells, Miami, especially Indian Wells, was not like that.
"I still obviously wasn't ready game-wise, physically. So Indian Wells and Miami were really kind of a struggle on the court for me mentally.
"I know that I can play much better than that, but I couldn't."