The twice Olympic 200 metres champion was suspended by her country's national federation last year following a positive test for a banned diuretic.
"I can confirm that Veronica Campbell-Brown has been cleared by CAS," Jacobs told Reuters by email.
"All of her past results have been reinstated and she is free to compete effective immediately.”
He said Campbell-Brown intended to compete at the world indoor championships in Poland next month.
The 31-year-old Campbell-Brown, who has won 16 Olympic and world championship medals, said she had suffered much in the last few months.
"However, my faith, family, friends and fans have stood by me as a source of encouragement," she said in a statement on her management company's website.
"The final court available to us as athletes have spoken and humbly I say they have confirmed my innocence.
"I harbour too much self-respect and a similar respect for the purity of competition to resort to illegal means to success.”
Campbell-Brown tested positive for the banned diuretic hydrochlorothiazide on May 4 at the Jamaica International Invitational World Challenge meet in Kingston.
She was provisionally suspended on June 18 by the Jamaican Athletics Administrative Association.
The JAAA disciplinary panel announced in October a public reprimand for the nine-times world championship medallist.
"Because the CAS hearing was completed on an extremely expedited basis, the full reasons for the award have not yet been issued, and may not be issued for a few months," Jacobs said.
"However, it is clear that the reason for the decision was a serious and fundamental breakdown in the manner in which Veronica Campbell-Brown's urine sample was collected and handled in Jamaica on May 4, 2013.
"The integrity of the sample was not maintained and the results of any testing on that sample were therefore unreliable.”
CAS has ordered the JAAA to pay a portion of Campbell-Brown's legal costs in connection with the appeal, he said.
"Veronica Campbell-Brown has maintained her innocence and her integrity throughout this long ordeal," Jacobs added.
Athletics ruling body the IAAF said it was still awaiting receipt of the full ruling from CAS.
"The IAAF was made aware earlier today of the CAS judgement but has not received the full reasoned decision and therefore will not make any comments about the decision at this stage,” spokesman Chris Turner said.
"We can, however, confirm that the athlete Veronica-Campbell-Brown is now free to compete.”
- Sports & Recreation
- Veronica Campbell-Brown