The former Conservative leader will instead become leader of the House of Commons and provide political advice to prime minister David Cameron until the end of this parliament.
Hague will not seek re-election to his Richmond constituency, which he has represented since the age of 28.
David Cameron said Hague would still play a key role in the government.
- Uber has suspended its low-cost UberPOP service in France following protests last week.
- After two previous missions failed, Russia's Progress rocket took off to resupply the International Space Station ?
- BP has agreed to pay a $18.7 billion fine to settle legal actions over the 2010 Deepwater Horizon oil spill.
- Liberia has reported three new cases of Ebola this week. The country was declared Ebola-free on May 9.