The Glasgow-born pair, both 19, have penned two-and-a-half-year deals and will play initially for the Under-21s.
Striker Jack, has played four league games for Doncaster, while central defender Paul has made one appearance in the Johnstone's Paint Trophy.
"It's a massive club. As soon as I heard Leeds wanted to bring us here, I said 'yes' straight away," Jack said.
"I've played with my brother for a long time and we know each other's game well," he told the club website.
"It works especially well with him being at the back and me being up front. I can make runs and I don't even have to call for the ball from him.
"He knows how I play and I know how to make runs for him. He knows where I'll be."
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Leeds United have signed teenage twins Jack and Paul McKay from Doncaster Rovers for undisclosed fees.