That makes five free agents on defense and six on offense or special teams that have decided to stay with Cincinnati. The Bengals' only notable signing from outside the team has been backup quarterback Josh Johnson, who will compete for the job that opened when Bruce Gradkowski signed with Pittsburgh as a free agent.
Jones played in every game during the Bengals' playoff season last year, starting five. He also returned punts and had an 81-yard touchdown return.
"It has been a pleasure to have Adam on our team," Darrin Simmons, the Bengals' special-teams coordinator, said in a statement. "He's an explosive player. He's got great innate talent. And he's competitive. He's tough. He'll fight you. He wants to succeed like crazy."
Tate caught 13 passes for 211 yards and a touchdown. He also returned 32 kickoffs for an average of 24.8 yards, and had 21 punt returns for an average of 8.9 yards.
Information from The Associated Press was used in this report.