Tlaib will fill the seat formerly occupied by Michigan Democratic Rep. John Conyers, who left office a year ago amid accusations of sexual misconduct.
In Minnesota, Omar, about 36 and a naturalised American citizen and state representative, follows another trailblazer: She will succeed US Congressman Keith Ellison, who in 2006 became the first Muslim elected to Congress and is stepping down to run 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 is the daughter of Palestinian immigrants and became the first Muslim female member of Michigan's state legislature a decade ago. Omar, a refugee from Somalia, is the first Somali-American Muslim woman to hold public office.
She spent four years in a refugee camp before coming to the United States at age 12.
"I made a decision 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.
Another Muslim woman, Ilhan Omar, who is running in Minnesota's 5th District, is also expected to win. Ellison was the first Muslim elected to Congress, in 2006.
US Muslim civil rights groups say a lot of anti-Muslim rhetoric comes from the media, as well as the country's political establishment. Tlaib favors a one-state solution to the Israeli-Palestinian conflict and has opposed United States aid to Israel.
Omar worked to fight hunger before becoming elected to the state's legislature since 2016.
Omar campaigned on a similarly progressive platform, which calls for universal healthcare and tuition-free colleges. She also has been mindful of the historic nature of her candidacy. She could not speak English and only learnt by watching television.