Unofficial, final results show the 61-year-old Turner beat King by more than 4,000 votes in Saturday's runoff. Turner's campaign was endorsed by President Barack Obama.
Houston hasn't elected a Republican mayor in more than 30 years.
Mayor Annise Parker was term-limited after six years in office. She's leaving under the disappointment of voters last month rejecting an anti-discrimination ordinance she championed. Parker was Houston's first lesbian mayor.
Turner lost a run for mayor in the 1990s but went on to carry unusual influence as a Democrat in Texas' Republican-controlled Legislature. Turner supported the repealed ordinance that would have established nondiscrimination protections for gay and transgender people.
Bill King concedes race in tight mayoral runoff election