Jones won the Democratic primary special election to finish the rest of Conyers' term, but lost the race for the 13th District full two-year term by about 900 votes.
Omar, who arrived in the U.S. at the age of 14 after fleeing civil war in Somalia and lived in Kenya's Dadaab camp, campaigned on a platform which called for universal healthcare and tuition-free colleges.
In 1995, they emigrated to the United States, initially settling in Arlington, Virginia and then moving to Minneapolis.More news: Three Red Sox players earn Gold Gloves
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.
"We did this, together", she wrote on Twitter Tuesday night.
She is not only the second Muslim women elected in Congress but also the first Somali-American.More news: Lines Long as Americans Render Midterm Verdict on Trump
Omar is running in Minnesota's strongly Democratic fifth congressional district.
She immigrated to the United States at age 12 and served as a Minneapolis City Council policy aide before winning election to the Legislature in 2016.
Her parents were Palestinian immigrants from the West Bank and Jerusalem.
"I'm Muslim and black", the hijab-wearing Omar said in a recent magazine interview.More news: Polls are open! Election Day 2018 is underway in Chicago