Warriors had to make do with a Challenge Cup spot last season but enjoyed a fine run to the final where they lost out to Toulon.
Warriors have been drawn in Pool 3 alongside Toulon, Aviron Bayonnais, Exeter Chiefs and Northampton Saints.
Munster are also in Pool 3, but Glasgow won't face their URC rivals as per the competition's new format.
Speaking in The Times, Smith said: "Our return to the Champions Cup is something that everyone at the club, from players to backroom staff, is really looking forward to in 2023-24.
"Toulon and Exeter are two top teams with whom we are more than familiar from recent seasons and who have great European pedigree.
"Northampton are a highly experienced team in European rugby who play a very expansive style, and Bayonne will be looking to show what they can do on their first appearance in the tournament.
"We are excited by the challenge that our group will present, and we know that we will need to be at our best on every match day in order to give ourselves the best chance of progressing from our group."