The suspects were taken to a central London police station where they remain in custody.
Two of the men were arrested at Manchester airport where they were due to fly to Pakistan and the third was arrested in a house in Leeds, the northern city that was home to three of the suicide bombers.
Searches were also under way on Friday at five houses in the area of Leeds and two premises in east London.
Police kept up a low-key presence on the streets as officers searched five properties in the ethnically mixed Beeston area of Leeds.
The three arrested men, aged 23, 26 and 30, are not suspected of being key players in the bombings, or of having directed the attack or assisted in making the backpack bombs, said an informed British security expert, who requested anonymity in return for discussing details of British counter-terrorism work.
Stephen Kamlish, a lawyer, said Muktar Said Ibrahim, one of the suspects, had visited Pakistan at the same time as two of the July 7 bombers.
No one has yet been charged in connection with the attacks, in which all four bombers died.
The head of London's anti-terrorist branch said last year police were chasing several leads in Britain and abroad as they tried to find anyone who may have been involved in the planning of the attacks.
The UK government has said that the four bombers were probably led by Mohammad Sidique Khan, the oldest of the group.
Two of the bombers had attended training camps in Pakistan in the run-up to the bombings and they were suspected of having links to fighters there.
Terrorism experts say attacks are often co-ordinated by a handler or a planner, and that it was very unlikely that a group of self-starting activists operating without any backing would be successful.
They also say the explosives believed to have been used would have required an experienced bomb maker.