"Throughout the modern world" is Western-centric and incorrect, at least for the thumbs. Head-shaking is very common as a negative sign, and one suggestion is that it's related to the movements of babies declining milk.

As for the thumb-gesture; any extension of the thumb is considered offensive in Israel, and obscene in southern Sardinia. Also, when waggled in India it means "I disagree".

No-one can agree on the origin; perhaps the Roman arena, perhaps medieval business.

Source: Roger E. Axtell, Gestures: The Do's and Taboos of Body Language Around the World

As a point of clarification, what you are referring to is not sign language, but gesture and body language.

As used by linguists, "sign language" refers to a complex, rule-based set of manual movements combined with facial expressions in ways that produce grammatically structured content. Examples include British Sign Language, Japanese Sign Language, etc. There are also "sign systems," which also involve complex manual and facial movements, but whose rules borrow from other languages to reproduce the grammar of those languages. These include Signed English (borrows from English), International Sign (borrows from the user's native sign language), etc.

Gesture, however, is not based in the rules of any language and does not produce grammar. It is used to convey specific points of meaning (thumbs up) or emphasis (shaking fist). Not all cultures use gesture the same way, and what is common in one culture may be offensive in another.