The 29-year-old Wales international is Leeds's first signing of the summer transfer window under manager Daniel Farke.
"It is a massive club in the Premier League, where the club belongs, so I'm really excited to join and hope to have some exciting years together," Wilson, who has spent five years at Fulham, said in a statement.
Wilson played a key role for Fulham last season, scoring 11 goals in 41 appearances across all competitions.
A product of Liverpool's academy, Wilson made 66 appearances for the club's Under-23 side but featured only twice for the senior team and had loan spells at several clubs, including Bournemouth and Hull City, before joining Fulham.
Leeds open their Premier League campaign against Nottingham Forest on August 22.