According to Appendix A, Annals of the Kings and Rulers, under "The Kings of the Mark", Théoden "fell into a decline under the spells of Saruman":
2948-3019 17. Théoden. He is called Théoden Ednew in the lore of
Rohan, for he fell into a decline under the spells of Saruman, but was
healed by Gandalf, and in the last year of his life arose and led his
men to victory at the Hornburg, and soon after to the Fields of
Pelennor, the greatest battle of the Age. He fell before the gates of
Mundburg. For a while he rested in the land of his birth, among the
dead Kings of Gondor, but was brought back and laid in the eighth
mound of his line at Edoras. Then a new line was begun.
In the chapter called the "The Voice of Saruman", Pippin asks Gandalf about Saruman:
Will he shoot at us, and pour fire out of the windows; or can he put a
spell on us from a distance?
To which Gandalf replies:
The last is most
likely, if you ride to his door with a light heart. But there is no knowing what he can do, or may choose to try. A wild
beast cornered is not safe to approach. And Saruman has powers you do
not guess. Beware of his voice!
So Théoden fell under Saruman's spell, and Saruman's spell was his Voice. Wormtongue was at most an agent.
In the movie, it's explicitly a spell. Is it the same in the book?
The movie shows magic as a visible and unnatural power.
In the book, the world is in a state of perpetual decline, and older is better. Today, many people have a gift that allows them to persuade with words. You could say Saruman was one of the oldest and most powerful users of the Voice. To us in the Later Days, that would seem like magic.