Ghana won the match in Cape Coast 1-0, but could not overturn a 3-1 deficit from the first leg and Senegal march on to the finals.
The only goal of the game was scored by Charles Boateng after 30 minutes, but despite wave after wave of attack, the Black Satellites could not get the second score that would have sent them through on the away goals rule.
Senegal finished as runners-up at the last African Under-20 Championships in 2015 that they hosted, losing 1-0 to Nigeria in the final.
The 2017 African Under-20 Championships will be played in Zambia from February 26 to March 12.
South Africa hold a 2-0 lead over Lesotho going into the second leg of their final qualification match on Saturday.