Old English springan "to leap, burst forth, fly up; spread, grow," (class III strong verb; past tense sprang, past participle sprungen), from Proto-Germanic *sprengan (source also of Old Norse, Old Frisian springa, Middle Dutch springhen, Dutch Related: springen, Old Saxon and Old High German springan, German springen), from PIE *sprengh-, nasalized form of root *spergh- "to move, hasten, spring" (source also of 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.). Meaning "to cause to work or open," by or as by a spring mechanism, is from 1828. Meaning "to announce suddenly" (usually with on) is from 1876. Meaning "to release" (from imprisonment) is from 1900. Slang meaning "to pay" (for a treat, etc.) is recorded from 1906.