How soon after signing an agreement is it legally binding?

As soon as an agreement has been signed by all parties, in conditions that are fully legal, it starts being enforceable.

NOTE: This only applies if a contract doesn't have an effective date.

Most contracts, however, have an effective date. In other words: a date from which the contract starts being put into action.

However, although it might sound pedantic: the contract is legally binding from the moment when all parties have legally and correctly signed — it becomes legally binding for the effective date.