The 27-year-old right-back, who has made only two appearances this term, is eligible for Saturday's visit of Peterborough.
Boss Alex McLeish revealed he turned to Jara after failing to re-sign Alan Hutton from Aston Villa.
"We tried for Alan Hutton again but I think he's looking to see if there's anything for him in the Premier League," McLeish told Villa's official website.
"You've got to move as quickly as you can and sometimes an opportunity like Jara doesn't come around again.
"He's a very experienced full back and is a guy who works and trains full-on."
Jara, who arrived at The Hawthorns for £1.9m in 2009, said: "I was very keen to talk to Forest when I heard they were interested in signing me. They are a big club and everyone in my country knows about their history.
"I have enjoyed my time with West Brom but I came to England to play football and this is an opportunity that I could not afford to turn down.
"There is a big challenge for Forest to get into the Premier League and I would love to play a part in that."