Hamid Ali, one of the leading imams at the Al-Madina Masjid mosque in Yorkshire, applauded the bombers in a secretly taped conversation, according to the Sunday Times.
The imam praised them as the "children" of Abdullah al-Faisal, a Muslim cleric jailed for inciting racial hatred and murder.
During the investigation by the Sunday Times a reporter lived as a student among the Muslim community in Beeston, Leeds.
The area was home to three of the bombers - Mohammad Sidique Khan, Shehzad Tanweer and Hasib Mir Hussain.
During the investigation Ali was recorded saying: "What they did was good.
"They have warned that we are here, we Muslims. People have taken notice that we are here.
"They died so that people would take notice... big meetings and conferences make no change at all.
"With this at least people's ears have pricked up."
The Sunday Times reported that Ali denied praising the bombers when confronted by the newspaper.
Fifty six people died in the attacks last July.