Four-month-old Hassan and Hussein Benhaffaf, who were conjoined at the chest, underwent surgery at London's Great Ormond Street Hospital.
Consultant paediatric surgeon Edward Kiely said: "The twins are in intensive care and are sedated but stable. We are pleased with how the operation went."
The boys came from their home in the Irish Republic for the operation.
Their parents, Angie and Azzedine Benhaffaf, from East Cork, said: "The sun is shining today for our two little fighters, who have won the battle of their lives.
"Words cannot express the relief and love we feel for our two boys. We thank God, we thank the surgeons and the gifted team at Great Ormond Street Hospital, and we thank from the bottom of our hearts the Irish nation and everyone who prayed for our beloved twins.
