The 31-year-old was without a club since parting company with Feyenoord last season.
Heerenveen technical manager Ferry de Haan has confirmed the news.
“Alireza is a player with depth, variation in his game and the necessary international experience,” Ferry de Haan said. “He therefore has qualities that we can use well in our team. We are therefore pleased that we can count on him at least until the end of the season.”
Currently, SC Heerenveen is in a precarious position and ranked 15th out of 18 in the Eredivisie with 9 points from 11 games.