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The actor, who received an Oscar nomination for his performance in the 1981 film "Chariots of Fire", had died from a Parkinson's related illness, the paper said.
"It is with great sadness that the actor Sir Ian Holm CBE passed away this morning at the age of 88," his agent told the paper. "He died peacefully in hospital, with his family and carer. Charming, kind and ferociously talented, we will miss him hugely."
Holm began his career on stage working as part of the Royal Shakespeare Company and gained international exposure when he was cast as android Ash in the 1979 "Alien" film.
His role as an athletics coach in "Chariots of Fire" won him a British Academy film award (Bafta) and an Oscar nod for Best Supporting Actor, while he played Bilbo Baggins in two of The Lord of the Rings films, a role he reprised in the recent "The Hobbit" film series.