GLENDALE, Ariz. — Gov. Jan Brewer of Arizona, a Republican whose approval of controversial measures on immigration and abortion have repeatedly put her in the national spotlight, announced Wednesday that she would not run for re-election, ending speculation that she might seek a third term.

“There does come a time to pass the torch of leadership,” Ms. Brewer said during brief comments at an elementary school here. “After completing this term in office, I will be doing just that.”

Even though the Arizona Constitution limits governors to two consecutive terms, Ms. Brewer had lately talked of finding a way around the term limits. She was Arizona’s secretary of state in 2009 when the governor at the time, Janet Napolitano, left to become President Obama’s Homeland Security secretary. Under the state’s succession rules, this meant that Ms. Brewer got the top job.

This year, with a roster of candidates lining up to replace her, Ms. Brewer toyed with the idea of trying to stay in office, saying she could make a case in court that although she had served two terms, one of them was not an elected term, so it should not count.