The 24-year-old has been in negotiations with the Whites for days, with Leeds boss Uwe Rosler eager to bring him to Elland Road after being his manager at Griffin Park.
In fact, it was the German who brought Dallas into English football as he signed him from Belfast side Crusaders in 2012.
And now Rosler has repeated the trick by securing the international midfielder for his debut season assault on the Championship with Leeds.
The club website has said that Dallas, who scored his first international goal for his country against Qatar this May, has joined on a three-year deal with the option on a fourth.
The missing piece for Rosler?
A left winger has been a target for Leeds for much of the summer, with former Bees boss Rosler managing to strengthen other positions in the side without managing to pick up that elusive wideman.
Dallas had a strong season as part of a superb attacking Brentford side last year, playing 43 matches, scoring 8 times and assisting 2 goals. He missed seven matches early on with a thigh problem, but then featured in every other league game except one for his side, as they secured a playoff spot late on in the campaign.
The winger also netted Brentford's goal of the season against Fulham, and Leeds fans will be hoping to see a slice of that talent in the near future with the club confirming that Dallas could make his debut in Saturday's Championship opener against Burnley.