Covas studied engineering at the Polytechnic School of the University of São Paulo.
He was elected federal representative, mayor of São Paulo City (1983–1985), senator and twice Governor of the state of São Paulo (1994–1998 and 1998–2001). In 1989, he was the PSDB presidential candidate, receiving 11% of the votes. In the run-off of that election, he supported, like his party, Luís Inácio Lula da Silva.
He took a medical leave of absence on 22 January 2001, due to bladder cancer found during an operation to remove a prostate tumor.
He died later the same year. His successor was his deputy, Geraldo Alckmin.
He entered politics in his native city of Santos, in the state of São Paulo. He was a founder and member of PMDB (Party of the Brazilian Democratic Movement) and later PSDB (Brazilian Social Democracy Party).