"He's gone out there and excelled and played well and been impressive in all his opportunities," Morris said, according to the St. Petersburg Times. "He's been a guy who's been cool, calm and collected.
"I can go on and on about all the things that prompted me to have to go with Cody and have the confidence to put him out there."
Grimm won the job over fourth-year pro Sabby Piscitelli, who started 15 games at strong safety last season.
"There was definitely thought about Sabby," Morris said as the Bucs (2-0) prepared for Sunday's game against the Pittsburgh Steelers (2-0). "Sabby's played over there a little bit. He's the backup strong safety and he definitely would have went in if anything would have happened to Sean (Jones). ... He'll still be a significant part."
The NFL announced Wednesday that Jackson was suspended, effective immediately, for a minimum of one year without pay for violating its substance-abuse policy. It's the second suspension for Jackson, who missed the first four games of the 2009 season while serving a ban for a similar offense.
Jackson, 25, is the only defensive player in Bucs history to start every game in his first two seasons.
Morris, who coached Jackson as a defensive backs coach before being named Tampa Bay's head coach, said he had a brief chat with the player before he left team headquarters Wednesday.
"Personally, it's tough (on me)," Morris said. "Everybody in this room knows that."
Grimm, the son of Hall of Fame guard Russ Grimm and a walk-on at Virginia Tech, worked his way up the Bucs' depth chart during the preseason, moving from outside linebacker to safety. NFL.com's Steve Wyche reported during the preseason that Grimm's open-field tackling and coverage ability left an impression on Morris, who said during organized team activities that the rookie would make the team if his on-field progression matched his work ethic.
"You watch the kid go out there and perform and then you put him in different situations that you didn't see him in college and he performs the way he has so far," Morris said Thursday. "He's been a student of the game. The limited amount of errors that he has made as a rookie, it gives you a great feel about him. I want to see him go out and play."
The Associated Press contributed to this report.