Until now police have had the power to arrest only those suspected of committing an offence carrying a sentence of at least five years in prison.
The new law requires only that the police have reasonable grounds for believing that a person's arrest is necessary. This can include a suspect's refusal to give his name and address.
The changes are part of the Serious and Organised Crime Act 2005, which removes the distinction between arrestable and non-arrestable offences.
Offences that have until now been non-arrestable include impersonating a police officer, not stopping a vehicle when ordered to do so and making or selling an offensive weapon.
Police will in future be allowed to photograph suspects on the street where they have been arrested or issued with a fixed penalty notice, rather than back at a police station.
Hazel Blears, a Home Office minister, explained the change: "The introduction of a single rationalised power of arrest simplifies arrest powers.
"These tough new powers make a significant contribution to creating a modern, efficient police service equipping frontline officers with the tools they need to fight modern crime effectively and keep our neighbourhoods safe."