The Serbia international joined the Rome-based club in 2013 but had a one-year loan spell at Inter Milan last season, during which he scored three goals in 25 league appearances.
Spaniard Falque joined Roma in 2015 after a one-year stint at Genoa. He scored twice in 22 appearances last season.
"After discussions with our coach we spared no effort to buy Ljajic from Roma," Torino President Urbano Cairo said in a statement on the club's website. "He was one of our first objectives, so we're pleased to add him to (Sinisa) Mihajlovic's squad."
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(Editing by Peter Rutherford)
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