Smith, 24, is out of contract at the League One club and will move to Elland Road on July 1 after signing a two-year deal.
Smith shot to prominance last season when he scored against both Everton and Liverpool in Oldham's run to the FA Cup fifth round and he finished the campaign with 11 goals in 40 appearances.
He began his career as a trainee at Cheltenham after impressing at non-league Solihull, he earned a move to Oldham in 2011.
"I'm really pleased," McDermott told the club website. "I've known him for a little while.
"He's come on to the scene in a short space of time, and I like his background, the way he's been brought up, he's done his studying, he went to Oldham, he's played against some big sides and done very, very well.
"Matt's from a league below and we're looking for someone with potential, who can be better, can play in the team, and who the fans can take to."
Smith added: "I'm absolutely delighted. Once I heard of the interest from Leeds United I was over the moon.
"It's a massive club with a massive history and I'm looking forward to being a part of it.
"Growing up as a kid Leeds were an absolute powerhouse with the likes of Harry Kewell and Mark Viduka, that's what I remember from growing up.
"But knowing what I do now it's a huge club with a terrific fan base. And with what Brian did at Reading, which is obviously something that he will want to do here, everything is just perfect really."