They are being interviewed at police stations in Buckinghamshire, Oxfordshire, and central, east and south west London.
Officers are searching the properties where the arrests were made.
One man, 48, was arrested at a business address in east London.
The 43-year old woman and the 49-year old man were arrested at their home addresses in Oxfordshire and are being interviewed at separate police stations.
It takes the total number of arrests under Operation Weeting to 23.
The investigation was launched in January 2011 after the Metropolitan Police received new information from News International, the publishers of the News of the World, the Sun, the Times and the Sunday Times.
It is being led by deputy assistant commissioner Sue Akers and has 91 officers working on it.
Previous arrests under Operation Weeting include Ian Edmondson, the former News of the World assistant editor; Neville Thurlbeck, the former chief reporter; Neil Wallis, the former executive editor; Rebekah Brooks, the former News International chief executive; and Stuart Kuttner, the former managing editor.
Previous Operation Weeting arrests for conspiracy to pervert the course of justice include Cheryl Carter, the long-standing PA to Rebekah Brooks; Glenn Mulcaire, the private investigator; and Ross Hall, the former NOTW reporter.