In HILLARY CLINTON’s soon-to-be published book titled “Hard Choices,” she’ll reveal that the secret raid on terror titan Osama Bin Laden was SO SECRET she couldn’t tell hubby Bill – and afterwards even President Obama was surprised!

In a section of the hot new book, obtained by The ENQUIRER, she writes that after the raid – in which Bin Laden was killed by U.S. Navy SEALS – Obama as a courtesy began calling the four living ex-Presidents to tell them the stunning news before he went on national TV to tell the nation.

Hillary writes, according to the book: “I took that seriously, as President Obama found out…,” adding: “When he reached Bill, he began, ‘I assume Hillary’s already told you…’ Bill had no idea what he was talking about. They told me not to tell anyone, so I didn’t tell anyone.

“Bill later joked with me, ‘No one will ever doubt you can keep a secret!”

Meanwhile, Tuesday’s edition of the “Washington Post” reported that the May 2, 2011 raid was “expected to be central” to Hillary’s new memoir because it has “the potential to become of the most politically rewarding decisions of her tenure” as Obamas’ Secretary of State as she considers another White House run for 2016.

The massive 635-page book is being published by Simon & Schuster, which it calls Hillary’s “inside account of the crises, choices and challenges she faced during her four years as America’s 67th Secretary of State, and how those experiences drive her view of the future.”