Patrick Rock, who has been involved in Government policy on internet porn filters, was arrested by detectives from the National Crime Agency (NCA) over a "potential offence relating to child abuse imagery", a Downing Street spokeswoman said.
The 62-year-old was arrested at his home on February 13 and officers were given access to all IT systems and offices at Number 10, she added.
In a statement, Downing Street said: "On the evening of February 12 Downing Street was first made aware of a potential offence relating to child abuse imagery.
"It was immediately referred to the National Crime Agency (CEOP). The Prime Minister was immediately informed and kept updated throughout. Patrick Rock was arrested at his home in the early hours of February 13, a few hours after Downing Street had reported the matter.
"Subsequently, we arranged for officers to come into Number 10 and have access to all IT systems and offices they considered relevant.
"This is an on-going investigation so it would not be appropriate to comment further, but the Prime Minister believes that child abuse imagery is abhorrent and that anyone involved with it should be properly dealt with under the law."
The spokeswoman confirmed Mr Rock - who was deputy head of Downing Street's policy unit - resigned on February 12.
Downing Street confirmed Rock was one of the advisers involved in the Government's policy on internet filters to protect against child abuse images online.
Leading search engine companies Google and Microsoft agreed in November to introduce changes that will prevent depraved images from being listed in results for more than 100,000 searches.
A Downing Street spokeswoman said: "Patrick Rock was one of a number of advisers and officials involved in dealing with this issue but the work was led by somebody else, and decisions were taken by ministers."
Rock took particular responsibility for home affairs issues in the No 10 policy unit.
Rock, from West London was brought back into Downing Street by Mr Cameron in 2011 after the pair both worked in the Home Office under Michael Howard in the 1990s, the paper said.
An NCA spokeswoman declined to comment, stating it did not name suspects on arrest.