The prestigious fellowships were awarded to Professors Laura Machesky and Robert Insall, who head up two labs researching cell movement at the institute in Glasgow.
Professor Machesky said: "It's an honour to have my group's contributions to cancer science in Scotland recognised by the Royal Society of Edinburgh.
"It's especially pleasing that Robert has also been awarded a fellowship at the same time.
"Our success is a fantastic endorsement of the strength and cooperative nature of the Beatson Institute and our hard-working colleagues."
Professor Machesky is the leader of the migration, invasion and metastasis group, and studies the mechanics of how cells move and potential drugs can stop cancer cells from spreading.
Professor Robert Insall leads the cell migration and chemotaxis lab. His group works on the genetics behind what drives cells to move, for example, out of tumours and around the body.
The couple, who have three children, met in the US at the Johns Hopkins Hospital in Baltimore.