Richard Branson Reveals How His Wife Died

Richard Branson is opening up about the death of his beloved wife ... revealing Joan -- who he'd been with for 50 years -- passed away after suffering a back injury.

The British business tycoon wrote an emotional tribute to Joan on Instagram, saying she was hospitalized in England while recovering from her back problems. Richard said he was recovering in the same hospital from injuries he suffered in a separate bike accident in India.

Richard said they laughed about "how typical it was for them to end up on the same floor" of the hospital ... and enjoyed a "lovely lunch" just before her death.

He described Joan as being in "positive spirits and getting stronger," as she "smiled at me, that radiant smile that lit up her whole face," which made him fall in love with her a half-century ago.

Then Richard said Joan was suddenly gone -- "quickly and painlessly" -- adding he was right by her side as she passed ... along with their 2 kids, Sam and Holly.

Everyone is devastated, Richard says, but he noted he's "grateful for the extraordinary gift of the life we shared - with our remarkable kids."

Branson first announced Joan's death on IG Tuesday, calling her the "most wonderful mum and grandmum our kids and grandkids could have ever wished for."

Joan was 80.