British Transport Police (BTP) response officers PC Gary Reader and PC Matthew Linley saw the woman on the wrong side of the barrier at 4.30am one morning last September.
They immediately pulled over, ran across and clutched hold of her.
The woman was trying to get out of their grip to jump into the River Aire – but the officers forcibly lifted her back over the barrier.
PC Reader said: “In regards to our own personal safety, I think at the time your instinct kicks in.
“You see the incident in front of you and you just think, ‘I’ve got to go and help that female’.
“At one point I was sat half on the parapet of the bridge which now, thinking about it, was probably a silly idea, because if she was going to jump she would have taken me with her.
“Obviously, there is always a risk to our own personal safety, but that’s not what you think about first.”
The woman was detained under the Mental Health Act and taken to St James’s Hospital, where she was treated.
PC Reader was handed an Award of Excellence from the BTP Federation on behalf of the Leeds pair at a ceremony in Cardiff on Tuesday because his colleague was unable to attend.
But PC Linley said it was “quite humbling” to be nominated for the award.
“I was just carrying out the course of my duty, just doing my job and so to have recognition for doing the job is quite pleasing,” he said.
Nigel Goodband, chairman of the BTP Federation, said: “Their courageous actions and quick-thinking ensured that the situation was brought to a safe conclusion for everyone involved.”