Alfred Barlow, 96, from Stockport, Greater Manchester, was returning home from a pilgrimage to Normandy, France, earlier this month where he fought on the beaches more than 70 years ago.
His wife and grandson carer noticed that his medals were missing after he visited the gents' toilets at Norton Canes Services, near Walsall, on the M6 Toll on Thursday June 8.
Crimestoppers has offered up to £5,000 for information that leads to the recovery of all four medals and the arrest and conviction of the person or people responsible.
Lord Ashcroft, the chairman of Crimestoppers, said: "After such a moving and poignant trip to Normandy, to lose or have stolen his war medals has been incredibly distressing for this brave former soldier.
"Whilst the actual value of the medals is nominal, the sentimental value is enormous.
"Our reward reflects the war veteran's invaluable service to our country."
The reward is in addition to a £1,000 offer made by actor Hugh Grant to reunite Mr Barlow with the 1939-1945 Star, the France & Germany Star, the 1939-1945 War Medal and the Palestine Medal.
Mr Barlow, who celebrated his birthday last Sunday, served with 3rd Reconnaissance (Recce) Regiment, 3rd Division, and landed on Sword Beach at 10am on D-Day, June 6 1944.
He said: "I have found it all very distressing.
"These medals are worth very little to sell but to me they are priceless.
"I had intended to pass all of my medals on to my grandson which makes it even more upsetting."
Anyone with information is asked to call Crimestoppers anonymously on 0800 555111 or the Blind Veterans UK hotline on 0800 389 7979.