The company, which also owns Flannels and Jack Wills, among others, will buy back up to £70m and the programme is due to end on 8 December when it reports its half-year results.
At 1005 GMT, the shares were up 3.3% at 689.50p.
Russ Mould, investment director at AJ Bell, said: "Frasers, rumoured to be among the bidders for collapsed online sofa seller Made.com, pleased investors with news of a £70m share buyback.
"The capital return on its own is pleasing but it also says something about the financial strength and robust outlook for the business despite a difficult retail backdrop."
