The Swiss is the oldest man to be number one, aged 36.
Roger Federer became the oldest number one singles player in tennis history after beating Robin Haase in the ABN AMRO World Tennis Tournament quarter-finals in Rotterdam on Friday.
The 36-year-old Swiss, who won his 20th grand slam last month by claiming a sixth Australian Open title, replaced Rafael Nadal at the top of the ATP rankings with a 4-6 6-1 6-1 victory over Dutchman Haase.
Federer has surpassed Andre Agassi as the oldest player to occupy the summit of the men’s game – the American was 33 when he was last on top in September 2003.
— ABN AMRO WTT (@abnamrowtt) February 16, 2018
He will now meet Andreas Seppi in the semi-final after the Italian saw off Daniil Medvedev 7-6 (7/4) 4-6 6-3.
Second seed Grigor Dimitrov is also through to the last four after a comfortable win over Andrey Rublev.
The Bulgarian won 6-3 6-4 thanks to a break in each set and he now faces fourth seed David Goffin.
Grigor Dimitrov is solid on serve to reach the Rotterdam semi-finals where he'll face David Goffin – a repeat of the 2017 #NittoATPFinals title match.
— ATP Tour (@atptour) February 16, 2018
Belgian Goffin advanced without even having to step on court as his last-eight opponent Tomas Berdych withdrew through to illness.
In Buenos Aires, Dominic Thiem set up a a semi-final clash with Gael Monfils at the Argentina Open.
The world number six triumphed 7-6 (9/7) 6-4 over home favourite Guido Pella, while Monfils saved three of five break points as he defeated another Argentinian, Leonardo Mayer, 6-4 3-6 6-3.
Meanwhile, Slovenia’s Aljaz Bedene upset fifth seed Diego Schwartzman in straight sets, winning 6-4 6-4 as he bids to advance to his third ATP World Tour final.
He will face Federico Delbonis in the semi-final, who battled past 34-year-old Guillermo Garcia-Lopez 6-3 7-5 after one hour and 25 minutes on court.
Kei Nishikori rallied from behind to beat Moldovan Radu Albot 4-6 6-3 6-1 and progress to the semi-final at the New York Open.
The world number 27 will meet top seed Kevin Anderson in the last four, after the South African eliminated American Frances Tiafoe 6-3 5-7 6-4 in two hours and four minutes.
Second seed Sam Querrey lost just six points on serve as he defeated 38-year-old Ivo Karlovic 7-6 (7/5) 7-6(7/4).
His semi-final will feature fourth seed Adrian Mannarino, following his win over Adrian Menendez-Maceiras 7-5 2-6 6-3.