Chapman was also selected to his ninth All-Star team and became the all-time leader in strikeouts by a relief pitcher, surpassing Hoyt Wilhelm's record of 1,363.
Eckersley noted the physical dedication required for the 38-year-old to sustain his trademark velocity.
"I've seen what he does. His workouts and stuff.
He's a monster," said Eckersley.
"It's hard to throw strikes when you throw that hard, he uncoils, he's got a lot going on.
It's impressive, though. You have to want to do it, he's not afraid."
Chapman's improved control has been key to his recent success, allowing him to complement his triple-digit fastball with refined command.
"It's not that easy just because he throws 100, it can't be, because you have to control that (expletive)," said Eckersley.
"And he's had his — he can lose it. When he was with the Yankees it could be a little scary.
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Until last year, he didn't walk anybody last year.
So it goes to show you what he can do if he has good control, it's like ridiculous."
The debate over relief pitchers and Hall of Fame candidacy continues, with only nine relievers enshrined in Cooperstown.
Billy Wagner was the most recent closer elected, in his final year of eligibility.
"How do you get to the Hall of Fame? 400 saves?
The last guy was (Billy) Wagner and it took him forever, so I don't know what the pecking order really is," said Eckersley.
