Calderwood was named Hibs' new manager last month and, after securing his first win in charge with a superb 3-0 win at Rangers on Wednesday, he now has a new assistant.
"This is a fantastic opportunity for me to come to a club of the stature of Hibernian," Adams told Hibs' official website. "In particular I'm looking forward to working closely with Colin Calderwood and the talented group of players at the club.
"I've had three magnificent years at Ross County and leave there with a sense of pride. The club made great progress over that period but it's now time for both Ross County and me to look forward to the next phase. I wish the club every success in the future."
Commenting on the addition of Adams to his staff, Calderwood said: "I'm delighted to have secured Derek's services and now feel that we have an extremely strong group of coaches at the club.
"I have been hugely impressed by Derek's achievements at Ross County and also saw in his Ross County team the type of organisation and dynamism that I want to see at Hibernian. I have no doubt that he will make a strong contribution to our future development."
County have also confirmed Adams' departure and chairman Roy MacGregor has thanked the 35-year-old for his efforts and endeavours while at the helm.
"I would like to thank Derek for all his hard work and leadership during his spell as Ross County manager," said MacGregor.
"He ensured a place of honour in the club's history by taking us to the Scottish Cup final last season and his tenure has also seen success in the Scottish Football League, including promotion to the First Division in 2008.
"I am sure every Ross County supporter will join me in wishing Derek every success in the future. As a board, our priority now is to identify the right candidate to help lead this ambitious club to the next level."