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.
- A University of Cincinnati officer has been charged with murder for shooting Samuel Dubose, an unarmed black man.
- Regulators are looking into allegations of "deceptive or unfair" marketing practices at the University of Phoenix.
- Mullah Omar, the Taliban's reclusive leader, died more than two years ago, Afghan officials say. The Taliban hasn't commented.