38-year-old Menefee, who has represented District 18 since February, defeated 78-year-old Green, who has represented District 9 since 2005.
Those who live in District 18 have cast votes for their representative four times in less than a year.
Sheila Jackson Lee held the seat for almost 30 years before she died in office in July 2024.
Then, former Houston mayor Sylvester Turner won the seat, but he died just two months after being sworn in.
Governor Abbott scheduled a special election in November 2025 to fill the remainder of that term. That delay left the district without representation in Congress for months.
Menefee won a special election in January after a runoff election, but then came redistricting in 2025.
The new congressional lines drastically changed Green's longtime 9th Congressional District, drawing his home into a brand new 18th district.
Neither Menefee or Green won a majority of votes in the primary, which led to Tuesday's runoff election.
Menefee will now face Republican nominee, Ronald Whitfield, this November.
Polls show the district is expected to be won by a Democrat.