Dr. Knight and Dr. Pritts -- the physicians who provided round-the-clock care for the Bills safety following the on-field incident -- announced the update just minutes ago ... saying they are thrilled with the improvements he's made in such a short amount of time.

The docs say 24-year-old Damar was up and walking ... and exhibiting his usual sense of humor prior to being released from the hospital. He will now go to a Buffalo facility, where he will undergo further testing.

The docs say they wanted Damar's condition to improve to "fair" or "good" before traveling ... and he met that criteria Monday morning.

As we previously reported, the Bills played in Hamlin's honor against the Patriots on Sunday ... and #3 was watching from his hospital room.

In fact, the docs say Hamlin was jumping up and down when teammate Nyheim Hines ran the opening kickoff back for a touchdown ... which set off all the alarms in the ICU.

The docs say they traveled with Hamlin to the airport on Monday ... and while the development is a step in the right direction, it's still too early to discuss his football future.

"He still has a little bit of a ways to go in terms of his ongoing recovery," Dr. Knight said. "We're thrilled to where he is today. He's up, he's walking around, he's got an amazing, genuine sense of humor and his family is amazing and we're happy he's with them but in terms of any kind of conjecture to his future, that's still significantly in the future and it's gonna be up to Damar and a great team of physicians to help him."

Hamlin sent out a tweet to his supporters following the news ... saying, "Headed home to Buffalo today with a lot of love on my heart."

"Watching the world come together around me on Sunday was truly an amazing feeling."