The midfield pair were made available for transfer by Black Cats boss Steve Bruce after he strengthened his midfield over the summer with the acquisitions of Lorik Cana and Lee Cattermole.
Leadbitter and Edwards will now be reunited with former Sunderland boss Roy Keane at Portman Road.
Ipswich-bound: Sunderland duo Grant Leadbitter and Carlos Edwards on the move
Leadbitter has moved for a fee which could reach £2.6million while Edwards has joined in a deal which could reach £1.35m.
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