The Judicial Conduct Investigations Office (JCIO) said in a statement that Lord Thomas of Cwygiedd, the Lord Chief Justice, and Chris Grayling, the Lord Chief Justice, had investigated allegations against the four judges.
They concluded that it was an "inexcusable misuse" of court equipment and condemned the judges' conduct as "wholy unacceptable".
The material viewed did not include images of children and was not illegal, a spokesman added.
District Judge Timothy Bowles, Immigration Judge Warren Grant and Deputy District Judge and Recorder Peter Bullock have been removed from office.
A spokesman for the JCIO told the BBC that the judges would no longer be allowed to work in a judicial role.
He said: "As far as I'm aware the judges are not appealing the decision.