Dozens of politicians have already been arrested as part of the inquiry.
Mr Fachin was chosen at random from a shortlist of five Supreme Court judges.
He replaces Teori Zavascki, 69, who died in a plane crash on 19 January.
Mr Zavascki's plane fell into the sea in heavy rain near Paraty, some 250km (160 miles) south of Rio de Janeiro.
He was a well-respected judge and the Car Wash investigation gained much credibility when he was appointed to oversee it in the Supreme Court, says the BBC's Daniel Gallas.
Most recently, Mr Zavascki had been investigating executives from Odebrecht, Latin America's largest construction firm.
Odebrecht has admitted paying $1bn (£800m) in bribes to obtain contracts in 12 different countries.
One of Mr Fachin's first tasks will be to analyse the plea bargain deals struck with 77 Odebrecht executives.
Local media say their testimonies could contain the names of high-ranking politicians allegedly involved in the bribery scheme.
Mr Fachin, a law professor from Parana state, was appointed to the Supreme Court by former President Dilma Rousseff, who was impeached in August.
Local media accused him at first of being very close to Ms Rousseff and her Workers' Party, citing as evidence a video, which showed him campaigning for her during the election.
But reaction to his nomination on Thursday was largely positive with commentators saying that he had "shown independence".
Brazil's Supreme Court has announced that Judge Edson Fachin will be in charge of cases resulting from Operation Car Wash, an investigation into a massive corruption ring involving some of Brazil's top business executives and politicians.