No Republicans ran in Tuesday's District 13 primary race, meaning Tlaib was set to win the seat the election and begin serving a full two-year term in January.
For Tlaib, Tuesday's election marks the second time she will have made history in recent years.
"I stand here before you tonight as your congresswoman-elect".
She added: "I think people don't realise just how much of a roller-coaster it is and its happy chaos right now".
In her victory speech, Omar's first words were: "As-salam alaikum" - a standard Muslim greeting that means "peace be upon you" - and then "alhamdulillah", or "all praise to God". She has said she'll push for universal Medicare, a $15 minimum wage, sustainable environmental policies, public school funding and fair immigration policies. After fleeing the country's civil war, she spent four years in a refugee camp before coming to the USA when she was 14.
Her expected takeover of the top post of the House's Africa panel will probably not result, however, in major shifts in United States policy.
Duchess Harris, a professor of American studies at Macalester College in St. Paul, Minnesota, and author of "Black Feminist Politics from Kennedy to Trump", said Omar's win is "a tremendous success for the people of the 5th District".
But the president escaped a feared "blue wave" as his Republicans bolstered their Senate majority after a polarizing, racially charged campaign.
Rashida is also the first Palestinian-American woman in Congress. She used that record of taking on corporate interests and defending local priorities as part of her campaign for election as a congressional representative.