"I stand here before you tonight as your congresswoman-elect".
She is not only the second Muslim women elected in Congress but also the first Somali-American.
Miski Omar, a high school senior who attended Omar's election night party, said she thinks Omar's election is inspirational for young women of color.
USA elects record number of women to House
In split-gender races, women have won 65 races and lost 101, but this is not necessarily a strong indication of gender bias. Democrats were galvanized by #MeToo movement, which helped attract female voters and recruit more women to run for office.
Palestinian-American Rashida Tlaib was another Muslim woman elected to the US Congress. New Mexico's Deb Haaland and Kansas attorney Sharice Davids were elected the first two Native American women to serve in Congress.
Omar's family fled Somalia in 1991 due to civil war.
Omar addressed key points she plans to address in Congress to a crowd brimming with supporters on Tuesday.
"It is a district that is very much interested in making sure our progressive values are represented", she said in an interview with MinnPost.
In an interview with Elle magazine in September this year, Ms Omar opened up about her Somalia background and shared what it was like to arrive in the U.S. for the first time as a child of 10.
Meanwhile in the Senate - the upper chamber of Congress - it looks likely the Republican Party will hold a majority with 51 seats against the Democrats' 43.
Only two other Muslims have been elected to Congress, and both are men now in office: Ellison and Indiana Democratic Rep. Andre Carson.