The 31-year-old arrives as coach Hansi Flick strengthens his goalkeeping options following Marc-Andre ter Stegen's loan move to Ajax earlier this month.
Livakovic, who has signed for a fee of two million euros ($2.33 million) plus half a million in add-ons according to Marca, is expected to compete with first-choice Joan Garcia, while veteran Wojciech Szczesny provides further back-up.
The Croatian joins Barca after two seasons at Fenerbahce, where he made 74 appearances and kept 24 clean sheets. He previously had a successful spell with Dinamo Zagreb, winning multiple domestic titles before moving to Turkey in 2023.
A regular for Croatia since 2017, Livakovic has represented his country at three World Cups and two European Championships.
He becomes Barcelona's sixth signing of the transfer window following the arrivals of Anthony Gordon, Karim Adeyemi, Jesse Bisiwu, Rodri and Joao Cancelo.
Barca host Athletic Bilbao in LaLiga on Thursday after starting their title defence and bid for a third successive crown with a 5-0 win at Elche last weekend.