Forest did not disclose any financial details, although British media reported the deal for the 22-year-old was worth about £34.3 million.
Diomande, a product of Danish club Midtjylland's academy, joined Sporting in 2023 and quickly established himself as a key figure.
He made 132 appearances in all competitions for the Lisbon side, helping them win back-to-back Primeira Liga titles in 2023/24 and 2024/25 plus the 2024/25 Portuguese Cup.
He also represented Ivory Coast at this year's World Cup, where they were eliminated by Norway in the round of 32.
"Ousmane is a powerful, commanding defender, and arrives here with a winning mentality. He shares the same ambition for success we have, and we are excited to see the impact he can have in a Forest shirt," the club's Chief Football Officer George Syrianos said in a statement.
Forest, who finished 16th in the Premier League last season, appointed Austrian Oliver Glasner as manager in July as they look to rebuild ahead of the new campaign.
They begin the league season at home to Leeds United on August 22nd.
As the summer transfer window ramps up, Flashscore has everything you need to keep up with breaking news, rumours and analysis. Follow our live transfer blog to follow the biggest moves, whilst expert Dean Jones will be on hand to provide the inside stories from around the world.