Frank Gifford -- Family Donates Brain ... 'He Suffered from CTE'

Kathie Lee Gifford says her late husband Frank Gifford suffered from a traumatic brain injury most likely caused during his NFL career ... and has donated his brain to be studied.

Gifford -- an NFL Hall of Famer -- died back in August at the age of 84 ... and now the Gifford family says he was diagnosed with CTE (a progressive degenerative brain disease) before he passed.

But the Giffords don't appear to hold a grudge with the NFL over Frank's condition -- saying they SUPPORT the league ... just as Frank did.

The family says they're donating Frank's brain "in hopes of contributing to the advancement of medical research concerning the link between football and traumatic brain injury."

The Giffords say they hope Frank's brain can be a "small part of the solution to an urgent problem concerning anyone involved with football, at any level."