CAS revealed it had signed agreements with the governing bodies of four Winter Olympic and three Summer Olympic Federations.
The International Triathlon Union (ITU) became the first federation to sign up with the CAS ADD in March.
The ITU was followed by the International Ski Federation, the first winter body to reach a deal with the CAS ADD, which became operational in January.
World Archery, World Rowing, the International Shooting Sport Federation, the International Luge Federation and the International Bobsleigh and Skeleton Federation have all since agreed to hand over their anti-doping matters to the Division.
The CAS ADD was set up in part to complement the work of the International Testing Agency and offer a choice of options for parties who make appeals.
Previously temporary anti-doping divisions have been established by the CAS during major events, including the Olympics, to deal with disputes during the Games.
CAS also said it had opened the offices of the ADD and had laid the foundation stone of the building that will house its future headquarters on the site of Beaulieu in Lausanne.
The ADD is currently housed at temporary offices but is due to move into the main CAS headquarters in 2021.
CAS revealed the budget for the construction of its new headquarters amounts to CHF35 million (£28.5 million/$35 million/€32 million).
The building will include three courtrooms and a 90-seat auditorium.