O'Grady, who is the TUC's deputy general secretary, was the only candidate nominated by unions and will become general secretary sesignate at the 144th Congress in Brighton this September.
She said: "This is a great honour. Never has a strong responsible trade union movement been so needed. With austerity policies biting hard and with no evidence that they are working, people at work need the TUC to speak up for them.
"We must be the advocates of the growth and jobs alternative. And with the policy prescriptions of the last thirty years increasingly discredited, we have the best opportunity in a generation to help build a fair, productive and green economy that works for ordinary people.
"Brendan has been a great servant of the TUC, well-respected both within and beyond our ranks. He leaves a firm foundation on which to build."
John Cridland, CBI director-general, said: "I would like to congratulate Frances on her appointment as TUC General Secretary. I'm sure she will provide the union movement with strong leadership in challenging times.
"In my dealings with Frances, I have always found her to be a powerful advocate for fairness, opportunity, and the modern workplace."
O'Grady will be the first woman General Secretary of the TUC. She has been an active trade unionist and campaigner all her working life. She has been employed in a range of jobs from shop work to the voluntary sector. Before the TUC, she worked for the Transport and General Workers Union where she worked on successful campaigns to stop the abolition of the Agricultural Wages Board and for the introduction of a national minimum wage, equal pay for women, and on a range of industrial wage claims.