The pair, along with Peter Tork, have performed as the pop group The Monkees since the 1960s.
Jones suffered a massive heart attack and died in his adopted home of Florida Wednesday morning. He was 66.
"I am in a state of shock," People.com quoted Dolenz as saying in a statement Wednesday. "Davy and I grew up together and shared in the unique success of what became The Monkees phenomena. The time we worked together and had together is something I'll never forget. ... He was the brother I never had and this leaves a gigantic hole in my heart. The memories have and will last a lifetime. My condolences go out to his family."
Jones is survived by his wife, Jessica Pacheco-Jones, as well as three sisters, four daughters and three grandchildren, People.com said.
Michael Nesmith, an original member of "The Monkees" who left the band in 1970 but returned briefly in the 1990s, also issued a statement mourning his friend.
"So many lovely and heartfelt messages of condolence and sympathy, I don't know what to say, except my sincere thank you to all," E! News said Nesmith told fans in a statement.
"I share and appreciate your feelings," he said. "While it is jarring, and sometimes seems unjust, or strange, this transition we call dying and death is a constant in the mortal experience that we know almost nothing about. I am of the mind that it is a transition and I carry with me a certainty of the continuity of existence. While I don't exactly know what happens in these times, there is an ongoing sense of life that reaches in my mind out far beyond the near horizons of mortality and into the reaches of infinity.
"That David has stepped beyond my view causes me the sadness that it does many of you. I will miss him, but I won't abandon him to mortality. I will think of him as existing within the animating life that insures existence. I will think of him and his family with that gentle regard in spite of all the contrary appearances on the mortal plane. David's spirit and soul live well in my heart, among all the lovely people, who remember with me the good times, and the healing times, that were created for so many, including us. I have fond memories. I wish him safe travels."