The TV presenter and former newspaper editor paid £2,600 for the unusual piece of history.
The cigar was left behind by Churchill on his voyage aboard HMS Duke of York in 1941 to meet American President Franklin D. Roosevelt.
It was auctioned by Trevanion and Dean in Whitchurch and had been expected to fetch about £1,000.
Auctioneer Aaron Dean said: "Similar cigars have sold for the £1,000 region at auction in recent times so I estimated the piece at £600 to £1,000.
"The cigar was featured in the national press and as such, caught the eye of keen Churchill fan, journalist and broadcaster Piers Morgan.
"Piers was delighted with his purchase and messaged us to express his joy at acquiring such a historically important artefact for his collection.
"We hope he enjoys being its custodian. It's gone from being owned by one PM to another, very different, PM."
After the auction on Saturday, Mr Morgan took to Twitter to tell his followers about his purchase.
He said: "I feel so patriotic today that I just bought Sir Winston Churchill’s half-smoked wartime cigar at an auction."
Another military piece sold for a world record price following a fierce bidding war.
A Grana British Army Watch, circa 1945, was bought by an international buyer for £9,000.
The unassuming wristwatch is one of the most popular and collectable military watches, according to auctioneer Christina Trevanion.
She said: "The WWW series of watches, or the ‘Dirty Dozen’ as they are popularly referred to, were the first to be specifically designed and custom made for the British Army.
"The watch was brought in to me during one of our routine valuation days here at Trevanion from a lady who lives near Nantwich. There have only been seven Grana watches sold at auction since 2012, and the prices realised have ranged from between £3,500 and£5,500. Ours had suffered some damage so I was modest in my expectations.
"The seller was absolutely delighted when I telephoned her after the auction to let her know the result. That watch has been sitting in a drawer for the last decade, so there is a lesson to us all – you never know what you might have squirrelled away. It is often the most innocuous looking things that have the most value in the current market."