Akufo, 30, was part of Kotoko's first team for the 2016-17 Ghana Premier League season but decided not to renew his contract after it expired in August but Adam on the other hand, arrived from El Egtmaeey, after his club suffered relegation from the Lebanese Premier League.
Akuffo expressed is happiness after completing the switch and wished Kotoko well in Ghana Premier League matches remaining.
"I'm happy with this opportunity and I hope things will work for me in Ethiopia," Akuffo told Success FM.
"I have paid my dues for Kotoko and I know the supporters will wish me well after I took this decision. It's left with only four games in the Ghana Premier League and I know they will do well to finish the season on a higher note because there are a lot of quality players still around. I thank everyone at the club for the support and prayers," he added.
Aside Akuffo and Adam, former Hearts of Oak player Kweku Andoh is also in Ethiopia with Dedebit FC.