Hendriks posted a video Wednesday on Instagram of him ringing the "victory bell" and a lengthy note thanking his medical team, wife, family, friends and fans.
"These past 5 months have been both the quickest and slowest of my life," he wrote. "Being able to ring this victory bell has been one of the most emotional things I've ever done."
Hendriks said his life "changed forever" five months ago.
"You never think you will be the one who hears 'you have cancer' but there I was ... in shock and fear not knowing what comes next," he wrote.
Hendriks announced the diagnosis in January. He said in a video shown Monday before the White Sox's home opener against the San Francisco Giants that he was beginning his final round of chemo.
There is no official timeline for Hendriks' return, although the White Sox elected not to move him to the 60-day injured list last month.
A three-time All-Star, Hendriks was third in the majors with 37 saves last season. He led the American League with a career-high 38 saves in 2021 after leaving the Oakland Athletics to sign a three-year, $54 million contract with the White Sox.
The Associated Press and Reuters contributed to this report.