"All of Brazil is in mourning, we lost a great Brazilian, we lost a great colleague," Xinhua quoted Rousseff as saying.
Earlier in the day, Campos died in a plane crash in Santos in southeastern state of Sao Paulo.
Campos's plane crashed over several houses in a residential neighbourhood in Santos.
We lost a great colleague, said Brazilian President Dilma Rousseff
According to the Brazilian Air Force, the plane crashed as it was preparing to land, and bad weather is likely to be the cause of the accident.
Campos had been politically active since youth, first as a federal deputy, then as minister and twice governor of Pernambuco state.
He was running in distant third place in the lead up to the Oct 5 general elections, behind Rousseff and Aecio Neves of the Brazilian Social Democratic Party.
In September, Campos, 49, abandoned the left-leaning government coalition headed by the Workers' Party to run as candidate of the Brazilian Socialist Party (PSB) on a platform that largely criticised Rousseff's economic policies.