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The draw for the competition was made in Monaco on Friday afternoon, with the Giallorossi selected in Group E alongside two domestic league champions.
Luciano Spalletti's side will now make trips to the Czech Republic, Austria and Romania over the coming months.
“We do not think about an easy draw or a difficult draw, you have to rise to the challenge,” general manager Mauro Baldissoni told reporters.
“The only thing we are happy about is avoiding some of the long journeys that, when you play on Thursdays, can create logistical problems.”
Viktoria Plzen, the side from Pot 1 in the group, are the reigning Czech champions - having successfully defended their domestic title in 2015-16.
They lost out in the final qualifier for this season's Champions League to Ludogorets Razgrad. Last season they also competed in the Europa League group stage, failing to progress from a group that included Villarreal, Rapid Wien and Dinamo Minsk.
Austria Wien, meanwhile, have a proud record in domestic football, having won the league title on no fewer than 24 occasions. They finished third in last season's Austrian Bundesliga.
The fourth team in Group E, Astra Giurgiu, are the reigning Romanian league champions - and knocked out Premier League side West Ham in the final play-off round to reach the group stage this year.
Specific match dates have also been finalised:
Thursday 15 September: Viktoria Plzen v Roma
Thursday 29 September: Roma v Astra Giurgiu
Thursday 20 October: Roma v Austria Wien
Thursday 3 November: Austria Wien v Roma
Thursday 24 November: Roma v Viktoria Plzen
Thursday 8 December: Astra Giurgiu v Roma
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