Villa, relegated from the Premier League and under new manager Roberto Di Matteo, will travel to Kenilworth Road during the week commencing August 8.
Newcastle and Norwich, also relegated from the top-flight, have been handed byes into the second round as they were the highest-placed teams last season.
Sheffield Wednesday, winners in 1991, will travel to League Two side Cambridge and 2013 finalists Bradford will play at Accrington.
Fleetwood have a home tie against Leeds, relegated Doncaster will play four-time winners Nottingham Forest and Derby take on newly-promoted Grimsby.
Two-time winners Wolves face Crawley at home and Jaap Stam’s Reading host Plymouth.
Brighton welcome Colchester, Swindon travel to QPR and Leyton Orient take on Fulham in a London derby.
The draw for the EFL Cup first round in full: