The 23-year-old signed a two-year deal after opting not to extend his stay with the Ghana Premier League champions and was declared a free agent by the Ghana FA's Player Status Committee on Friday.
Darkwah believes he has achieved one of his dreams and wants to be a success in Kumasi.
"It is a great feeling to be here and be part of a great club like Kotoko. Actually, it is a dream comes true," Darkwah told Goal.
"A lot of things have gone on but I'm glad I'm back and hope to have a positive impact here. The stakes are high but I believe I have the qualities to match it," he added.
Kotoko have been billed to face Congolese side CARA next month and Darkwah believes they would have a good run in the competition.
"I'm aware of the club's ambitions to achieve success in the Caf Confederations Cup and with the players available, I'm optimistic that we will get far in the competition. We just need some time to work things out and everything will be awesome," he said.
Darkwah was spotted at the club's training ground on Sunday when Kotoko defeated second-tier side Rainbow FC 3-0 in a friendly.