He said would quit as party leader once arrangements were in place to choose his successor, potentially triggering another round of Conservative infighting as MPs scramble to replace him.
Starmer will become prime minister after a Conservative rout that resulted in former premier Liz Truss and a host of cabinet minister losing their seats.
In a statement outside No.10 on Friday, Sunak said: "I will shortly be seeing his majesty the King to offer my resignation as prime minister.
"To the country, I would like to say first and foremost, I am sorry.
"I have given this job my all, but you have sent a clear signal that the government of the United Kingdom must change. And yours is the only judgment that matters.
"I have heard your anger, your disappointment, and I take responsibility for this loss."
After 648 of the 650 Commons seats had been declared, Labour had a majority of 176.
Labour had 412 seats and the Tories 121.
"Following this result I will step down as party leader - not immediately, but once the formal arrangements for selecting my successor are in place."It is important that, after 14 years in government, the Conservative Party rebuilds, but also that it takes up its crucial role in opposition professionally and effectively," Sunak said.
"This is a difficult day at the end of a number of difficult days, but I leave this job honoured to have been your prime minister.
"This is the best country in the world. And it is thanks entirely to you, the British people, the true source of all our achievements, our strengths and our greatness."
After speaking in Downing Street, Sunak travelled by car to Buckingham Palace to resign as prime minister.
Buckingham Palace confirmed the King had accepted his resignation.
Starmer will go to see the King to accept the responsibility of forming a government.
