Katsav, who could now face years in prison, had denied charges he twice raped an aide when he was a cabinet minister in the late 1990s, and molested or sexually harassed two other women who worked for him during his 2000-2007 term as president.
But a three-judge panel said his testimony had been "riddled with lies."
"When a woman says no, she means no," the panel said in its ruling.
Katsav was also convicted of obstructing justice, for trying to confer with one complainant about her testimony to police.
The ashen-faced 65-year-old had no comment for reporters as he was spirited out of Tel Aviv District Court by a scrum of relatives, attorneys and bodyguards.
One of his lawyers, Avigdor Feldman, criticized the unanimous verdict for ignoring "all of the doubts" about the women's accounts and said Katsav planned to appeal the ruling to the Supreme Court.
State Attorney Moshe Lador praised Israel's legal system, saying that few countries would have prosecuted their head of state for such crimes. "Positions of power cannot grant immunity to criminals, however senior they may be," he said.
"This is a sad day for the state of Israel and its residents," Prime Minister Benjamin Netanyahu, said in a statement after the verdict.
"Today the court conveyed two clear-cut messages, that all are equal before the law and that every woman has exclusive rights to her body," Netanyahu said.
Rape carries a minimum prison term of four years and a maximum of 16 years in Israel. Moshe Negbi, legal analyst for Israel Radio, told Reuters any sentences handed down to Katsav for the lesser charges would probably be served concurrently.