Nadal and Federer have not met at Wimbledon since their epic 2008 final, which the former won in five sets in one of the great contests of all time.
The No. 3 seed needed only three sets and just over two hours to down the unseeded American.
Nadal battled through a tough first set that lasted almost an hour before eventually running away with the final last-eight clash on No. 1 Court.
Querrey, 31, was a big underdog for Wednesday's clash, as he had lost four of his five meetings against Nadal.
It already looked a long way back for the world No. 65 when he was broken early on in the opener, but he broke Nadal with some brilliant returning to tie up the set at 5-5.
Unfortunately for Querrey, to combat Nadal he was having to go for the lines with every shot, and in the next game his accuracy deserted him and he was broken again.
At the second time of asking, Nadal duly served out the opening set, but only after saving three more break points:
Querrey was again put on the back foot early in the second when Nadal broke for a 2-1 lead after two stunning winners off either side and a phenomenal drop shot.
Nadal looked increasingly unstoppable as he got a racket to everything Querrey could throw at him, and the world No. 2's remarkable defence secured him a double break for 5-2.
A backhand smash in the next game gave him a 2-0 lead.
Querrey's race was all but run, and a stunning piece of misdirection at the net gave Nadal a break and 1-0 lead at the start of the third set.
Another break for 4-1 put Nadal on the brink of a seventh Wimbledon semi-final, and he completed the victory with a forehand winner to set up a mouthwatering matchup against Federer.