Amarfio, who became CEO in November 2019, tendered his resignation to the board on Friday.
The Kangaroos collected their second-straight wooden spoon this season following a 2-20 campaign that accompanied a grim percentage of 55.8.
Coach David Noble was sacked in July after just 38 games at the helm, while football department boss Dan McPherson and assistants Heath Younie and Anthony Rocca left recently.
Since last reaching the finals in 2016, North Melbourne have finished 15th, 9th, 12th, 17th, 18th and 18th in a disastrous rebuild.
Four-time premiership coach Alastair Clarkson's arrival on a five-year deal has been hailed as a huge coup as the Kangaroos attempt to claw their way back into finals contention.
Club president Sonja Hood was the driving force behind luring Clarkson, while Amarfio was set to be in charge of plan B if the Hawthorn great chose not to come.
Amarfio played a key role in helping North become debt free for the first time in almost 35 years during his three years as chief executive.
But the horrible on-field results in recent years drew huge criticism.
Amarfio said the past few months "had taken a toll" on him, and he was looking forward to a break.
"On-field, we have undergone a major re-build and bold list turnover," Amarfio said in a statement.
"Turning around our AFL program has been extremely challenging. Year two of our rebuild has proven harder than we envisaged and we weren't as competitive as we had expected.
"As CEO, ultimately that responsibility lays with me and I'm sorry that we let down our members and supporters and fell short of expectations this year.
"However, I am excited about the talented young list that we are building and I think the time is right for me to step aside and provide clear air for Alastair Clarkson, Todd Viney and our hard-working and talented football department to begin their important work, which will hopefully see us getting back to finals and winning silverware in the coming years."
Amarfio said the club is forecast to finish the year with cash reserves of about $3 million and a membership tally in excess of 50,000.
Three years ago, the club was in debt and had only 38,000 members.
"We have zero historical debt, we've broken membership records in each of Ben's three years," Hood said of Amarfio's contribution.
"Ben's greatest and most long-lasting legacy will be the Arden Precinct vision he led and fought for so strongly from the moment he walked through the doors.
"Present and future North Melbourne players, officials, members and supporters will enjoy the fruits of that work for generations to come and it has paved the way for the club to be embedded in North Melbourne for the next 150 years."
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