Old English springan "to leap, burst forth, fly up" (class III strong verb; past tense sprang, past participle sprungen), from Proto-Germanic *sprenganan (cf. Old Norse, Old Frisian springa, Middle Dutch springhen, Old High German springan, German springen), from PIE *sprengh- "rapid movement" (cf. Sanskrit sprhayati "desires eagerly," Greek sperkhesthai "to hurry").
In Middle English, it took on the role of causal sprenge, from Old English sprengan (as still in to spring a trap, etc.). Slang meaning "to pay" (for a treat, etc.) is recorded from 1906. Meaning "to announce suddenly" (usually with on) is from 1876. Meaning "to release" (from imprisonment) is from 1900.