Martz was Vermeil's offensive coordinator when the Rams won Super Bowl XXXIV with Kurt Warner earning game MVP honors. Martz became head coach and hired Smith as his defensive coordinator, and the two helped guide the Rams to Super Bowl XXXVI, which they lost to the New England Patriots.
"He's a brilliant football coach," Vermeil said on "The Afternoon Saloon" on ESPN 1000. "He's a great gameday coach. He's as good as it gets as an offensive coordinator.
"When he came in on his first offensive coordinator job ever in the National Football League in 1999, the job he did has never been duplicated or was done before him. To take a quarterback off the street [Warner was working in a grocery store in 1994 after getting cut by the Green Bay Packers] and helped him earn Most Valuable Player in the National Football League ... is a testament to Mike Martz."
Vermeil said if Bears quarterback Jay Cutler has the right mental makeup, he could flourish under Martz.
"He's a brilliant football coach and a tough football coach, and it takes a tough-minded quarterback to handle the type of coaching he's going to get," Vermeil said, "but I'm sure you've got one there, and I think it's a positive.
"I think Mike will do a great job of working with Lovie Smith. They've done it before together, taking a team to the Super Bowl. Lovie Smith has made some good decision here in the past, this is probably his best one."
Vermeil also addressed the perception that Martz ran Warner out of St. Louis.
"I was with Kurt Warner in Arizona one night ... he said there was as a lot of things [said] about why he left the Rams, [such as] Mike Martz ran him out of town," Vermeil said. "He said he would play for Mike Martz again tomorrow."