For the past four years Barnes has been joint md of the discount retailer in the UK and Ireland, alongside Roman Heini.
Heini will leave his position to take up the role of chairman of the advisory board for Aldi South, which is based in Germany, in April.
‘Outstanding leadership’
A statement from the group said: “We would like to thank Heini for his outstanding leadership and contribution to our success in the UK and Ireland.”
When Barnes takes on the top role on April 1 2014, he will be supported by two new joint mds for the group.
Earlier this month, Aldi pledged to create 35,000 new jobs over the next eight years in a £600M expansion that could boost its store numbers to 1,000.
Earlier this year, an Aldi customer found a dead lizard in a 39p vacuum-packed cucumber bought from a store in Cowes on the Isle of Wight.