The 33-year-old joined Inter from Genoa in 2012 and has played 132 matches for them, scoring 54 goals. He has netted only once in 13 appearances this season.
"There's nothing like playing for this club. I'm delighted and I can't wait to be involved in the big matches this season has in store for us," Palacio said.
Inter play sixth-placed Sassuolo on Sunday.
(This version of the story corrects Palacio's age to 33 in third paragraph)
(Reporting by Bartosz Dabrowski in Gdynia, editing by Ed Osmond)
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