The 24-year-old White was invited to participate in a rookie camp this weekend.
White led the Oklahoma Sooners to national championship games in 2003 and 2004 but he had surgery on both knees and some scouts said he did not have a strong enough throwing arm for the NFL.
"I just want to give it a shot," White told the Kansas City Star Thursday.
"We're excited that Jason has an opportunity to pursue his goals and know that he'll make the most of this opportunity," Oklahoma Coach Bob Stoops said.
"He has proven time and again that he can succeed at the highest level."
Chiefs General Manager Carl Peterson said: "He's an extraordinary young man. You can't count him out. He's as tough-minded as anybody and he's had some great stats."