Jara Reyes, capped more than 50 times by his country, is scheduled to train with his new team-mates on Friday and the right-back will be in the Forest squad for their Championship fixture against Peterborough at the City Ground on Saturday.
Reds chairman Fawaz Al Hasawi said: "Gonzalo boasts vast experience of football at both club and international level and I'm sure he will be a fantastic addition to our squad. I'm delighted to welcome him to the City Ground."
Jara Reyes began his career in his homeland with CD Huachipato and Colo Colo before attracting the attention of West Brom.
He moved to The Hawthorns in the summer of 2009 in a £1.4 million deal and helped the Baggies clinch promotion to the Premier League in his first season at the club.
The 27-year-old made more than 30 appearances for Albion during the 2010/11 campaign and had two loan spells with Brighton last season, playing 14 times.
Meanwhile, Forest have recalled goalkeeper Karl Darlow from his loan spell at Walsall after just 10 days.
The 22-year-old, who had a previous stint with the League One side earlier in the season, was scheduled to remain with the Saddlers throughout January but has been brought back by boss Alex McLeish to bolster his options between the posts.
Darlow trained at the club's Nigel Doughty Academy on Thursday morning and will be available for selection at the weekend.