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The two sides will face each other in a one-off tie in mid-August, with the winner set to progress to the final of Round 1 of the competition.
The winner of the tie will face either Paris FC or Servette in the final - with a place in Round 2 up for grabs to the winner of that one-off contest.
Glasgow are regular Champions League participants, having twice reached the quarter-finals of the competition.
They finished second in the Scottish top flight last season, behind Rangers.
"Glasgow City are a great side, with their physicality being perhaps their biggest strength," Roma Women coach Alessandro Spugna said.
"It's not their first experience in the Champions League, so we are going to have to be very focused and at our best.
"It was great to finally see Roma's name in a draw for the Women's Champions League. We need to make sure we enjoy the experience but we also need to go into it with a bit of recklessness too - we need to do everything we possibly can to go as far as possible in the competition."
Imperium Partners
Centurion Partners
