Brandt: Top undrafted players
Keenum, who wasn't drafted, will vie for playing time behind starter Matt Schaub and backup T.J. Yates.
"I wanted to come to the Texans for a long time now," Keenum said. "I'm really glad it happened. I truly believe it's a first-class championship franchise and look forward to being part of a whole lot of championships in the years to come."
"If other teams had seen him work out for us, he would have been drafted," Kubiak said. "He was a sponge when I was telling him things. He picked them up right away."
Keenum is the NCAA's all-time leader in passing yards with 19,217 and in touchdown passes with 155.