Graham Dudman, former managing editor of The Sun, and its picture editor John Edwards chose to sever ties with the paper.
"The past three years have been an incredibly difficult time, and the right thing for me and my family is to now move on to a fresh start," said Dudman, who along with Edwards was given a choice of returning to the publisher or negotiating a severance deal.
They were both tried last year at Kingston Crown Court after News International (now News UK) handed over millions of internal company emails to Scotland Yard as part of its Operation Elveden investigation into payments to public officials for tips and stories.
Dudman was cleared of two charges while two other charges against him were dropped by the Crown Prosecution Service (CPS) months later.
He spent more than 20 years working on the tabloid in various roles, including Moscow correspondent, head of news, news editor, features editor and managing editor.
Edwards, 50, was cleared of two charges of conspiring to commit misconduct in public office. He had been with the Sun for 27 years, 15 of them as picture editor.
In all, 27 journalists were charged under Operation Elveden, the vast majority of them from the Sun.
A Court of Appeal ruling earlier this year quashing the conviction of a former 'News of the World' journalist and a prison officer had led to a review into the cases under the operation.
The decision led to CPS scrapping all but three journalists' trials, triggering fierce criticism of the 20-million-pound Operation Elveden.
