Saud, first named in 1975 and the world's longest-serving foreign minister, pledged to carry out his duties "with honesty, integrity and sincerity" as he was sworn in at the Yamamah Palace in Riyadh.
Saud, born in 1940, had been in the United States for back surgery when Salman acceded to the throne on January 23, replacing King Abdullah who died aged about 90.
Within days, Salman undertook a major government shakeup but left some veteran faces including Saud in their posts.
Over much of Saud's term in office, the kingdom maintained a focus on the West, while regionally it favoured opposition to "radical" regimes, experts say.
Under his watch the kingdom has also achieved growing international status, for example by joining the World Trade Organization.
Saud returned from the United States last week to host talks with US Secretary of State John Kerry.