United paid a nominal fee to take the 19-year-olds from League One with the intention of adding them to their development squad at Thorp Arch.
The Whites moved in to complete a deal after West Ham United agreed a fee for the Glasgow-born pair.
Steve Evans, who took an interest in the pair while in charge at Rotherham United, said the twins were joining as “Under-21 players not first-team players” and predicted further recruits of the same ilk as Leeds look to strengthen their development pool.
Centre-back Paul and striker Jack are the sons of well-know football agent Willie McKay and both players came through the youth-team system at Doncaster.
Jack, who won Doncaster’s academy player-of-the-year award in 2013, played four times for Doncaster’s first team including one start in a League One game against Notts County last season.
Paul made his only senior outing in a Johnstone’s Paint Trophy tie at Burton Albion earlier this term.
Evans said: “They’re signing as Under-21 players not first-team players and they be working mostly with Paul Hart (United’s academy director).
“We need to replenish our Under-21s for the simple fact that so many youngsters have moved up to the first team - Lewie Coyle, Lewis Cook and Alex Mowatt before them. That’s great for the first team but it weakens the development squad so you’ll see more signings like this.
“I looked at them when I was manager of Rotherham but I wasn’t able to do a deal. We heard that West Ham United had had an offer accepted so I sat down with the president (Massimo Cellino) and we agreed to match that offer. From there is was a decision for the boys.”
Evans admitted that the signing of brothers “probably looks unusual” but said: “They’re both good players in their own right. They’ve both got the attributes we want.
“It probably looks unusual and everyone would acknowledge that but other players like them will be joining us soon. We’re going to strengthen the academy because we have to strengthen the academy.
“But that doesn’t mean the likes of the Under-16s won’t be allowed to come through the ranks. The Under-16 squad has got some great talent in it and they’ll get their chance. We just need more resources.”