Ms Salih arrived in Scotland as a young girl, after her family fled Iraq, and as a teenager she became part of the Glasgow Girls campaign protesting against the dawn raids that were used to remove some failed asylum seekers.
She said she hoped her win on Friday will inspire other refugees to put themselves forward in future elections.
“The Glasgow people have always welcomed me,” Ms Salih told PA Scotland.
“This just shows that. I’ve never given up and now they’ve trusted in me.”
She added: “I can’t believe it. Twenty years ago I came to this country as a refugee, and to think back I would never have imagined to serve my city.”