The 2012/2013 Premier League champions attacked throughout the game to bury their opponents under an avalanche of goals.
The stadium went into a frenzy as skipper Mike Akuffo lifted the trophy.
It was Medeama who made early incursions to unsettle Kotoko but lacked precision upfront .
When the champions managed to warm themselves into the game, they seized control of the midfield and using the flanks to their advantage took the lead in the 24th minute through Seidu Bancey.
The Porcupine Warriors increased the tally five minutes later as defender Abeiku Ainooson sneaked past his marker to find the back of the net.
From recess, Medeama threw caution to the wind and marshalled more men upfront, however, the attack centred around Hans Kwoffie could not break the impregnable Kotoko defence.
Soon, substitute Yahaya Mohammed sealed victory for Kotoko in the 78th minute in a dramatic fashion.
It was a clinical finish from the midfielder who intercepted a pass, dribbled three defenders and let go a powerful shot, beating goalkeeper Foli Adade in the process. GNA