Really well ... at least, according to Josh.

Bradford got the hook Sunday after falling behind to the Bears ... in another lackluster start for the former #1 overall pick.

Rosen was thrown into the game with just minutes remaining -- and while he couldn't pull off a Baker Mayfield and lead his squad to a come-from-behind victory, he's officially been named the starter moving forward.

But there's no bitterness or hostility -- so says Rosen -- who thanked 30-year-old Bradford for being supportive at practice on Monday.

"Since day 1, Sam has had my back and helped me become the best quarterback I could be. I cannot thank him enough for showing me how to be a professional in every sense of the word."

"He is a leader, mentor, and great person. He and Mike Glennon couldn’t have been more supportive at a time that I thought might be a bit tense or awkward today."

"I couldn’t be more thrilled to be in a QB room with two of the most selfless people I’ve ever been around as I start my career as a quarterback in the NFL. For that I say thank you."

"With that being said, let’s get the valley rockin’ AZ!!!!"

Next up ... Seattle.