The 27-year-old Hungary international, who finished last season on loan at Manchester City having slipped down the pecking order at the Stadium of Light, moves to Portman Road for an undisclosed fee.
Fulop was signed for Sunderland by Keane and went on to make 50 appearances for the Wearsiders, including 14 last term.
Fulop, who has penned a two-year deal with Ipswich, trained with his new team-mates this morning and could make his debut against Middlesbrough in Town's npower Championship opener on Saturday.
As well as Keane and international colleague Tamas Priskin, there will be plenty of other faces familiar to Fulop at Portman Road.
Carlos Edwards and Grant Leadbitter have made the same move from the north-east on permanent deals.
Fulop arrived in England when he signed for Tottenham in 2004 but failed to make the grade at White Hart Lane and was loaned out to Chesterfield, Coventry and Sunderland before switching to the Black Cats permanently three years ago.
Further loan spells at Leicester and Stoke followed.