He joins on a free transfer after his City Ground contract expired in the summer.
As is becoming increasingly common in modern contracts, the Tigers have the option of extending his deal with them by a further 12 months in 2024.
The 28-year-old, who joined Forest in 2018, has played age-group football for Portugal at every level from under-15 to -23.
"Tobias is a brilliant guy and got amazing reviews from Forest," said vice-chairman Tan Kesler before the deal was officially signed off. "We've been following him closely because we wanted someone in our back line with experience to develop Jacob (Greaves), help Jacob to be where he's supposed to be. Alfie (jones) is next to him Sean (McLoughlin) is next to him so they're going to be a good group of people.
"I believe in our back line so much but we needed somebody with a little bit of experience and still having a winning mentality.
"We brought him in to help our back line to go on to the next level."
Coach Shota Arveladze added: “He knows our league and how to play in the Championship. He’s a solid and smart defender who is good in position.”
Figueiredo's final Forest appearance was actually at Hull in May, having been an unused substitute in each of the three play-off matches which took Forest into the Premier League, overcoming Sheffield United and Huddersfield Town.