Trinidad & Tobago international wide midfielder Edwards has signed a two year contract at Portman Road whilst central midfielder Leadbitter has signed a three year deal with the club.
The deal, whilst officially undisclosed, is thought to be for a fee in the region of £4M including both players who will now link up with Town boss Roy Keane for a second time, having both played under the former Republic of Ireland international during his time as boss at The Stadium of Light.
Speaking to the Official Club Website, Keane said: "I worked with both players at Sunderland and know what they are all about.
"They have dropped down from the Premier League to join us. That shows a hunger and commitment to play football for Ipswich Town and I'm delighted to have them here.
"They have played in the Championship, know what's needed to get out of this division and they will add qualities that we need at this football club."