Ms Tlaib, a Palestinian-American, secured Michigan’s 13th congressional district in a race in which she was the sole major party candidate, having won the Democratic primary earlier this year.
Meanwhile, in Minnesota’s Fifth congressional district, Somali-American Ms Omar bagged the seat previously held by Keith Ellison, the nation’s first Muslim congressman. Both women are Democrats.
Ahead of the race, Ms Tlaib told CBS: “The first thing I think about when somebody says you’re going to be the first Muslim is celebrate this moment. We changed the course of history at a time we thought it was impossible. And that if you just believe, believe in the possibility of someone like me.”
She added: “I think people don’t realise just how much of a roller-coaster it is and its happy chaos right now.”
Ms Omar, a Minnesota state congresswoman, ran a progressive platform that included “Medicare for all”, criminal justice reform and abolishing Immigration and Customs Enforcement, The Hill reported.
It said the Somali refugee came to the US at 12 years old. She has often spoken out against President Trump’s travel ban against Muslim-majority countries.
Ms Omar beat out five other Democratic contenders for Mr Ellison’s seat.
“We did this together,” Ms Omar tweeted. “Thank you!”