The 23-year-old Colombia international has moved to Elland Road for an undisclosed fee, believed to be in the region of €25m (£21.5m) plus add-ons.
Sinisterra becomes Jesse Marsch's sixth signing of the summer window after Brenden Aaronson, Rasmus Kristensen, Marc Roca, Darko Gyabi and Tyler Adams, the latter of whom joined the club from RB Leipzig on Wedensday.
Speaking to LUTV on his arrival in West Yorkshire, Sinisterra said: "I am very happy to be here in this beautiful club, I am enjoying this time.
"I know it's a historic club with beautiful fans. I heard a lot of things about the stadium and atmosphere, it's amazing so I can't wait to feel that in person.
"It was my dream when I was a child [to play in the Premier League], right now I am close to making that.
"Of course I will work to bring this quality (form with Feyenoord) to Leeds. This is my feeling, that I want to do the same or even more for this team and for the fans.
"I think it is also one of my characteristics, to enjoy and make the fans happy with my skills, my quality and hopefully I can do that here at Elland Road."
Sinisterra leaves Feyenoord after four years with the Dutch outfit, where he scored 23 goals and provided 14 assists in 49 appearances across all competitions last season.
The winger is seemingly viewed as a replacement for Brazilian star Raphinha, who has been strongly linked with a move to Barcelona, while Chelsea and Arsenal are also believed to be in the race for his signature.
Sinisterra could make his competitive debut for the Whites against Wolverhampton Wanderers on the opening day of the Premier League season on August 6.