WASHINGTON — Hillary Rodham Clinton formally resigned Friday as America’s 67th secretary of state, capping a four-year tenure that saw her shatter records for the number of countries visited.

In a letter sent to President Barack Obama shortly before she was to leave the State Department for the last time in her official capacity, Clinton thanked her former foe for the 2008 Democratic presidential nomination for the opportunity to serve in his administration. Clinton said it had been an honor to be part of his Cabinet.

“I am more convinced than ever in the strength and staying power of America’s global leadership and our capacity to be a force for good in the world,” she said in the letter.

Her resignation will be effective on the swearing-in of her successor, John Kerry, who was to take the oath of office in a private ceremony later Friday.

Clinton pushed through a throng of American foreign service workers who clamored for handshakes and smartphone photos with her and gave an emotional goodbye speech.

She told them to continue to “serve the nation we all love, to understand the challenges, the threats and the opportunities that the United States faces and to work with all our heart and all of our might to make sure that America is secure, that our interests are promoted and our values are respected.”