The 29-year-old made 26 Premier League appearances for Fulham last season and follows Morocco defender Issa Diop through the door from Craven Cottage this summer, in a deal reported to be worth around £9m.
Ipswich Town manager Gary O'Neil said the experienced midfielder's top-flight pedigree made him an ideal fit for the club's return to the Premier League.
"Sasa is a player who brings real experience to the squad heading into the new season," O'Neil said.
"Having played nearly 100 games in the Premier League, he knows what it takes to compete in the division and has been a consistent performer throughout his time at Fulham."
Lukić, who joined Fulham from Torino in January 2023 and went on to make 106 appearances for the Cottagers, said he was relishing a return to Portman Road having previously played there as an opponent.
"I can't wait to play here as a home player," he said. "I have played at Portman Road before in the Premier League and the atmosphere was one of the best I have experienced."
A 62-cap Serbia international who represented his country at both the 2022 World Cup and Euro 2024, Lukić began his career at Partizan Belgrade before spending seven seasons at Torino, where he made 168 appearances and scored 14 goals. He signs a contract with Ipswich running until the summer of 2030.