The men are being held on suspicion of being concerned in the commission, preparation or instigation of acts of terrorism under section 41 of the Terrorism Act 2000.
Metropolitan Police officers said the arrests were pre-planned as part of an ongoing investigation by the force's counter terrorism command and MI5, and that they were linked to activity in the UK.
Three of the men, aged 18, 25 and 27, were arrested at their home addresses in east London, while a 24-year-old was arrested near to his home address, also in east London.
They are in custody at a south London police station.
Officers have been searching five homes and a business in east London as part of their enquiries.
The current terror threat level in the UK is severe, the second highest, which means an attack is highly likely.