The officer, who was less than two years into his job, was one of the first on the scene after he responded to calls for help from the public after a vehicle ploughed into pedestrians on London Bridge.
BTP chief constable Paul Crowther, who visited the officer in hospital where he is in a stable condition after suffering face, head and leg injuries, said he showed “enormous courage in the face of danger”.
He said: “Although he is seriously unwell, he was able to recount how he faced the attackers armed only with his baton, outside London Bridge station.
“For an officer who only joined us less than two years ago, the bravery he showed was outstanding and makes me extremely proud.
“All of us at BTP wish him a swift recovery, and I know he will be touched by the hundreds of messages of support from across the UK and the world.
“Our thoughts are with all of those who died or were injured, and their loved ones as they try to come to terms with what happened.”
An off-duty Metropolitan Police officer was also seriously injured during the London Bridge attack, Scotland Yard said.
BTP said extra police would be patrolling stations in London and the South East in the wake of the attacks, with armed officers at stations.
A spokesman said: “We ask you to be vigilant and report anything that you see or hear which is suspicious, or just doesn’t feel right.”
Metropolitan Police Federation chairman Ken Marsh said: “I can confirm that sadly some of our colleagues were among the injured in the attack last night. I join all UK police colleagues in wishing them a swift recovery.
“We are offering them our full support.”
Mr Marsh added: “First and foremost our thoughts are with the families of those who lost loved ones in the horrific events last night and we wish well to those still injured.
“There can be no doubt that the swift response of our colleagues - both armed and unarmed - saved further lives from being lost.
“There are barely words to describe their bravery - officers who ran towards danger with no thought for their own safety.
“Londoners can rightly be proud of their emergency services today. They are the best of the best and we thank everyone for their praise and kind comments.”