Seven-time Wimbledon champion Federer will face either Canada's Milos Raonic, the sixth seed, or German 10th seed Alexander Zverev for a place in the semi-finals.
Raonic defeated Federer in the semi-finals at Wimbledon in 2016.
Federer, 35, is also the second oldest man to make the quarter-finals at Wimbledon behind Ken Rosewall who was 39 when he reached the last-eight in 1971.
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