The Bears claimed Orton after he was put on waivers by the Denver Broncos Tuesday, but Chicago instead signed McCown after the Chiefs' claim on Orton took precedence due to their worse record, the NFL Network reported.
McCown has a 57.7 percent career completion average with 6,584 yards, 35 touchdowns and 40 interceptions while playing for Arizona, Detroit, Oakland and Carolina.
Meanwhile, Orton, a former Bear, has been claimed by Kansas City, the broadcaster reported. Kansas City is seeking a replacement for injured starter Matt Cassel, who had hand surgery this week.
Orton became expendable in Denver after Tim Tebow claimed the starting quarterback job there.