The 24-year-old has put pen to paper on a three-year contract with the option for a further year after passing a medical on Monday and becomes Leeds’ seventh summer signing.
Dallas is expected to be included in the squad for Saturday’s opener against Burnley at Elland Road.
He had a year to run on his contract at Brentford but opted not to sign a new deal this summer.
The Northern Ireland international was signed by Brentford in August 2012 from Crusaders when Rosler was in charge of the west London club.
Dallas had a loan spell at Northampton in 2013 but returned to Brentford and was a regular last season as the club reached the Sky Bet Championship play-offs, scoring eight goals in 43 appearances.