Nadal moved up to second in the rankings following Casper Ruud's quarterfinal loss to Japan's Yoshihito Nishioka at the Korea Open on Friday. His compatriot Alcaraz, meanwhile, has been ranked No. 1 since his title run at the US Open.
"Momento histórico" (Historical moment), said Nadal.
Alcaraz had earlier expressed pride at being at the top along with someone of Nadal's stature, who was also a fellow Spaniard.
"Two (Spanish flag) at the top of the ranking! Proud to share this historic moment with @rafaelnadal, greatest player of all time! Let's go!" said Alcaraz.
"Dear Roger, my friend and rival; it’s been a pleasure but also an honor and privilege to share all these years with you" - Rafael Nadal's emotional message to Roger Federer following his retirement
Sharing arguably one of the biggest rivalries in the world of sport, let alone tennis, Rafael Nadal and Roger Federer never failed to produce exciting matches together. However, this was no ordinary rivalry filled with envy or ruthless competitiveness; instead, it was one that had warmth and friendship at its core.
Fans even coined the term 'Fedal' to describe the duo, which symbolized the love and respect that the players had for one another both on and off the court.
Following Federer's retirement announcement last month, Nadal took to Instagram to share some emotional words for the Swiss. The Spaniard also reminisced about the many "amazing moments" the two had shared together on and off the court.
"Dear Roger, my friend and rival. I wish this day would have never come… it’s a sad day for me personally and for sports people around the world. I said it to you when we spoke and now it’s here. It’s been a pleasure but also an honor and privilege to share all these years with you, living so many amazing moments on and off the court," said Nadal.
Nadal went on to wish Federer and his family all the best for what lay ahead, before stating that they would share more moments together.
"We will have many more moments to share together in the future, there are still lots of things to do together, we know that. For now, I truly wish you all the happiness with your wife, Mirka, your kids, your family and enjoy what’s ahead of you," added Nadal.