Dr. Bob Anderson performed the surgery in Charlotte, N.C., where Suggs will rehabilitate.
"We know he will work hard to get back on the field with his teammates as soon as the doctors and trainers allow," Newsome said. "We're confident that he can make a full recovery."
It's not known when he will be able to suit up this year, but Suggs said he could be back by midseason after the injury happened. Achilles injuries often require many months of recuperation.
Suggs said he became aware of the injury during a "stop-and-go" exercise.
Suggs, the reigning NFL Defensive Player of the Year, told the Carroll County Times that he was doing "sweet, marvelous" after the surgery, saying he got good news but did not elaborate.
The Associated Press contributed to this report.