McCown has replaced injured starter Jay Cutler, throwing for 538 yards and four touchdowns and no interceptions in his last three games, and he will continue to deputise against the Baltimore Ravens this Sunday.
The 34-year-old told Bears.com: "Sometimes everything in life is just about opportunities and when things happen. The timing of all of this for me in the stage of my career to get hooked up with these coaches and these players, I think it's just all coming together at the right time.
"It's energised me, no doubt about it, because it's fun to work with people that understand what they're doing and are going to put you in a chance to be successful. I'm very appreciative of everything that's going on right now."
The 5-4 Bears currently sit in second spot in the NFC North.