Bellingham was also given a one-match suspension in principle, but UEFA said that would not be immediately enforced and would be subject to a one-year probationary period.
Demiral mimicked the shape of a wolf's head with his fingers after his second goal in Turkey's win over Austria in the last 16. The gesture is linked to Turkey's far-right "Grey Wolves" group and was condemned as racist by Germany.
UEFA said he was being punished "for failing to comply with the general principles of conduct, for violating the basic rules of decent conduct, for using sports events for manifestations of a non-sporting nature and for bringing the sport of football into disrepute."
Demiral and Turkey's government have defended the gesture as a normal expression of patriotic pride.
In Bellingham's case, he kissed his hand and lowered it to his groin after the final whistle in England's last-16 2-1 over Slovenia.
His fine and suspended one-match ban were "for violating the basic rules of decent conduct," UEFA said in its statement.
"Said suspension is not immediately enforced and is subject to a probationary period of one year, starting from the date of the present decision," it added.
'Inside joke'
In the latest of a slew of sanctions against participating countries for fan misbehaviour, UEFA also fined the English Football Association 10,000 euros for crowd disturbances and 1,000 euros for lighting of fireworks during the Slovakia game.
There was no immediate reaction from England's FA.
Bellingham, who had been widely praised in the past for maturity beyond his years, said his gesture was not aimed at Slovakia, as some interpreted it, but as a laugh with friends.
"An inside joke gesture towards some close friends who were at the game. Nothing but respect for how that Slovakia team played tonight," he said hours after the game.
Amid the furore over Demiral's gesture, Turkey's President Tayyip Erdogan is planning to attend his nation's game in Berlin.
"Does anybody ask why the German national jersey has an eagle, or the French jersey a rooster? Merih (Demiral) showed his excitement with that gesture," he said on Thursday, according to Turkish media.
The "Grey Wolves", whose symbol Demiral evoked, is an ultra-nationalist youth branch of Turkey's Nationalist Movement Party (MHP), an ally of Erdogan's ruling AK Party.
Established in the 1960s, the "Grey Wolves" were involved in political violence between leftists and nationalists that killed some 5,000 people around the time of a 1980 coup.
The group is outlawed in France and its symbol is banned in Austria. It is also under surveillance in Germany.
Turkey's foreign ministry has defended the gesture as "a historical and cultural symbol" that Demiral used without targeting anyone at the game.
The symbol goes back to use by some Turkic tribes of Central Asia and also by Turkey after its foundation in 1923, but the hand gesture used by the player has been adopted by the MHP in recent decades.
England face Switzerland while Turkey play the Netherlands in the Euro 2024 quarter-finals on Saturday.