The draw, which took place at Hampden Park this afternoon, means that Aberden will face the Greenock club for the first time in the competition since 1996.
Due to AFC's challenge match against Viking Stavanger, the Morton game will be played on either Tuesday 21st August or Wednesday 22nd August pending permission being granted by the Scottish Football League.
To read Caddy Carhandle's review of the last time the Dons faced Morton in the League Cup, click here