"I ran because of injustices and because of my boys, who are questioning their (Muslim) identity and whether they belong", Tlaib said in an USA television interview in August.
Omar said President Trump's "politics of fear" motivated her to get in the race.
She is expected to share the honour with Somali-American Ilhan Omar, who was leading the opinion polls in Minnesota.
She also has been mindful of the historic nature of her candidacy.
She spent four years in a refugee camp before coming to the United States at age 12.
"I chose to run because I was one of many people I knew who really wanted to demonstrate what representative democracies are supposed to be", she said.More news: Nigeria's army cites Trump to justify shooting Shia protesters
Omar, a Somalia-born community activist and representative in the State House, is favored to win in November in the 5th District now held by Keith Ellison, who won the DFL primary for state attorney general.
Tlaib ran unopposed in Michigan's 13th district House race, but fended off a last-minute write-in challenge from a woman she defeated in the August primary.
Tlaib linked her campaign to the surge of female political activism in the United States following Trump's stunning 2016 victory, alluding to the millions of women that took to the streets of Washington and major cities across the country after his inauguration.
Technically, Palestinian-American Rashida Harbi Tlaib is the first American Muslim woman to be elected to Congress.
"We did this, together", she wrote on Twitter Tuesday night.
Tlaib is endorsed by the Democratic Socialists of America, a burgeoning left-wing group that also counts New York Democratic congressional nominee Alexandria Ocasio-Cortez among its members.