Omar, won fifth congressional district, replacing the first Muslim congressman, Keith Ellison, who vacated his seat to run in the state's attorney general race.
U.S. voters elected two Muslim women, both Democrats, to Congress on November 6, 2018, marking a historic first in a country where anti-Muslim rhetoric has been on the rise, American networks reported.
Omar was elected to the Minnesota House of Representatives in 2016, and she became the first Somali-American ever elected to state legislature.
Swift had said that the Republican's voting record in Congress "appalls and terrifies" her, stating that Blackburn had voted against equal pay for women and against protecting women from domestic violence.
She shared: "We changed the course of history at a time we thought it was impossible".
She is expected to share the honour with Somali-American Ilhan Omar, who was leading the opinion polls in Minnesota.
In recent interviews Tlaib has voiced support for a one-state solution to the Israeli-Palestinian conflict, slashing U.S. military aid to Israel and efforts to boycott the Jewish state.
Born in Detroit to Palestinian-American parents, Tlaib served in Michigan's state legislature from 2008 to 2014.
In addition to Omar and Tlaib, Tuesday's election saw several other historic firsts in the Democratic camp. She is also the first Somali American to win election to national office, according to CNN.
Democrats are celebrating Omar's win and the diversity in their party, but they may regret their choice after scrolling back through her Twitter timeline.
MA will also be getting its first black congresswoman while Arizona and Tennessee stand to elect their first woman senators.
On the program, she expressed hope that she and the new Congress, with a Democratic House, can serve as a check on the administration of President Donald Trump.