Stuart Mair, 59, has been suspended from the Canongate Youth Project, where he has worked for 30 years.
It is understood he was released on bail by police after files were discovered on a computer in his home.
The charges are understood to relate to one video clip allegedly of a paedophilic nature and another which allegedly contravenes new laws on extreme pornography.
A long-standing youth worker in Edinburgh, colleagues at the part council-funded group are said to be shocked by the allegations against Mr Mair.
It is understood the images were spotted on the computer when work was being carried out on his home.
Mark Harrower, of Wardlaw Stephenson Allan Solicitors, said on behalf of Mr Mair: “Stuart Mair voluntarily attended a police interview yesterday after which he was charged with the alleged possession and downloading of a video clip from the internet which is said to contain indecent images of a child.
“It is not suggested that the alleged finding of these images is in any way connected to Stuart Mair’s employment, nor is there any suggestion that there has been any inappropriate contact between Mr Mair and any child who attends or is connected to the Canongate Youth Project.
“Until such time as the clip itself and the circumstances of its recovery have been scrutinised by Mr Mair’s legal advisers, no further comment can be made.”
Mr Mair has been a senior figure at the charity for more than 20 years.
He has written articles on youth problems for newspapers and has featured in specialist education publications.
He was named Voluntary Organisation’s Youth Services Manager of the Year in 2008. He was given his award by the then Minister for Children and Early Years Adam Ingram.
Jamie Megaw, chairman of the charity, said: “I am aware of the charge made against a member of staff by Lothian and Borders Police. As a result this member of staff has been suspended with immediate effect. Canongate Youth Project will cooperate fully with the ongoing investigation by the police.”
Mike Rosendale, head of schools and community services at the city council, said: “We were very concerned to learn of the recent charges made against a senior member of the Canongate Youth Project’s staff and await the outcome of the police investigation.”
Mr Mair has been bailed and is scheduled to appear at Edinburgh Sheriff Court in May.
A police spokesman said: “A 59-year-old man has been arrested and charged in connection with alleged sexual offences.
“He is scheduled to appear in court at a later date.”
The Canongate Youth Project, based in Infirmary Street, offers a range of services to young people living in the Old Town, Southside, Holyrood and Dumbiedykes.
It offers support for young people between the ages of five and 21 with sexual health, alcohol or drug issues along with those having problems at school or home.
The charity also offers activity trips and help in gaining employment.
In the past it has been involved with local schools, working with pupils on boosting self-esteem and on anti-bullying strategies.