The 29-year-old becomes Leeds' first signing of the summer, almost a year after a proposed move to Elland Road collapsed on transfer deadline day. Wilson attracted interest from Aston Villa, Everton and clubs competing in the Champions League, while Fulham also offered him a new contract following the best Premier League season of his career.
Instead, the former Liverpool player opted to join Leeds, citing the club's determination to sign him.
"When the season finished and I became a free transfer, I felt Leeds were the team that really showed the interest in me," Wilson said.
"As a player, you want to play for a team which you feel like they want you and you feel like they are doing everything to get you."
Wilson admitted there was relief after the previous failed transfer.
"It was close last year and we got it over the line this year, so I'm delighted to be here," he said.
"I've played here numerous times as an away player and every single time it has been a tough game, an intimidating atmosphere and I'm looking forward to being on the other side of that."
Wilson, who has won 69 caps for Wales, scored 10 Premier League goals and provided seven assists in 36 appearances for Fulham last season. His 17 goal involvements were the most by a Fulham player in a top-flight campaign since Dimitar Berbatov recorded 18 in 2012-13.
He also finished as Fulham's leading scorer despite generating just 5.8 expected goals, while his 78 shots and 25 efforts on target were both team highs. Only Alex Iwobi created more chances for the Cottagers than Wilson's 39.
The move reunites Wilson with Wales team-mates Dan James, Ethan Ampadu and Joe Rodon at Elland Road.
Leeds are also pursuing Southampton midfielder Shea Charles and former Borussia Dortmund midfielder Julian Brandt, who is available as a free agent.
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