The 28-year-old finished his fifth season with Swansea earlier this month, but he declined their offer to take up United's deal of a three-year contract last week, four days before the League One play-off final.
Robinson told the YEP: "I made my decision last week and I knew then what the different possibilities were. Play-off finals are never predictable.
"The biggest factor was that I wanted to go to Leeds, and I accepted their offer when I did because it didn't matter to me whether I'd be playing with them in League One or the Championship. I just wanted to wear the white shirt.
"Sunday's match was about one season. I looked at the whole package with Leeds and thought more about what they can achieve in the future.
"I was a champion with Swansea and I know what it takes to get out of League One. I've no doubt that we'll do it at Leeds next season.
"They're a great club whatever division they're in, and I'm as proud to be joining them now as I was before Sunday."
Leeds initially made enquiries about the winger during the January transfer window while Dennis Wise was manager at Elland Road.
His three-year deal is expected to be officially signed on July 1.