Educated at the Royal High School and the Universities of Edinburgh, Leiden, and Paris, he took his doctor's degree at the University of Angers in 1662, and soon afterwards settled as a physician in Edinburgh. In 1667 with Sir Andrew Balfour he started the botanical garden in Edinburgh, and he took a leading part in establishing the Royal College of Physicians of Edinburgh, of which he was elected president in 1684.

In 1685 he was appointed the first professor of medicine at the University of Edinburgh. He was also appointed Geographer Royal in 1682, and his numerous and miscellaneous writings deal with historical and antiquarian as well as with botanical and medical subjects.

Sibbald's historical and antiquarian works include:

• A History Ancient and Modern of the Sheriffdoms of Fife and Kinross (Edinburgh, 1710, and Cupar, 1803)
• An Account of the Scottish Atlas (folio, Edinburgh, 1683)
• Scotia illustrata (Edinburgh, 1684)
• Description of the Isles of Orkney and Shetland (folio, Edinburgh, 1711 and 1845).

The Remains of Sir Robert Sibbald, containing his autobiography, memoirs of the Royal College of Physicians, a portion of his literary correspondence, and an account of his manuscripts, was published at Edinburgh in 1833.

Originally the Blue Whale was named after Sibbald, who first described it scientifically. The wildflower Sibbaldia procumbens also was named after him.

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