The 27-year-old has agreed a one-year deal with the club holding the option of a further year.
Benda made just four appearances for Fulham across three seasons at Craven Cottage, all in cup competitions, spending last season out on loan at Millwall and Feyenoord, where he made a combined 12 appearances.
A product of Swansea City's academy after progressing there via 1. FC Heidenheim and TSV 1860 Munich in his native Germany, Benda made his professional debut on loan at Swindon Town in 2019-20, helping them win the League Two title, before returning to Swansea and eventually becoming their first-choice goalkeeper for the 2022-23 season, making 23 appearances before a serious knee injury ended his campaign.
He moved to Fulham in 2023 but never established himself as a regular, prompting last season's loan moves.
Nottingham Forest chief football officer George Syrianos welcomed the signing.
"Steven is an experienced player who we feel will add depth and competition to our current group of goalkeepers," he said.
"Steven is someone who we know will work hard every day to push his teammates to keep standards high at the training ground, and we are sure he will fit in with the strong culture we have at the club."
The move comes with Forest having lost both Angus Gunn and Stefan Ortega from their goalkeeping department this summer, leaving head coach Oliver Glasner short of senior cover behind his first-choice option.
Benda's arrival follows the club's earlier capture of defender Ousmane Diomande, continuing a summer of targeted additions at the City Ground rather than wholesale changes to the first-team squad.
Forest are next in action against Stade Brestois in a pre-season friendly, giving Benda an early opportunity to press his case before the Premier League campaign gets under way.