Welbourn was left behind after being level at the half-way point and he was delighted with achieving a medal at his home Paralympics.
"I'm over the moon with that," he said. "I said this morning it would be a tough race and it really was.
"To come away from a home Games with a medal, I can't ask for any more.
"It was difficult to see what was happening. I could hear the crowd cheering as they have all week and it spurred me on."
ParalympicsGB added two more golds to their tally on day seven.