The England international has not played since he was arrested and later bailed at the start of March, but could now feature in Dick Advocaat's managerial debut against West Ham on Saturday.
Johnson's bail was subsequently extended on Tuesday as the allegation continues to be investigated and he does not have to report back to police until April 23.
A statement from Sunderland read: “The club has discussed the current position in detail with both the PFA and Adam’s representatives,” it said.
“In line with those discussions we recognise that the player is entitled to re-commence his duties with the club while the legal process continues. He will therefore return to training.
“The club’s own investigation cannot continue until the conclusion of the legal process. Sunderland AFC will make no further comment on the matter due to the ongoing police investigation.”
Durham Police added: “Sunderland AFC informed us this morning of their decision, which of course is a matter entirely for the club.”
“The police investigation remains very much live and ongoing and a man remains on bail while enquiries continue.
“We would once again urge those posting on social media to be aware of the effects their comments can have. We accept rumour and speculation may be inevitable, but many of the comments have been distressing to the complainant, her family and people connected with the investigation.”