Federer (20) and Nadal (22) have won a total of 42 major titles
The pair will represent Team Europe against Team World's Jack Sock and Frances Tiafoe at London's O2 Arena.
Before that match, Andy Murray will start the evening session in singles against Alex de Minaur at 19:00 BST.
Federer, a 20-time Grand Slam winner, said last week he would retire at the team event, which starts on Friday.
The 41-year-old Swiss said it would be "wonderful" to play alongside Spaniard Nadal, 36, who has 22 major titles.
"I'm not sure if I can handle it all but I'll try," said Federer.
"I have had some tougher moments as well in the past, being horribly nervous all these years sometimes before matches. This one definitely feels a whole lot different.
"Of course, it's super special playing with Rafa. I'm happy to have him on my team and not playing against him."
Nadal said he was looking forward to an "unforgettable" match with his rival against the American duo.
"One of the most important, if not the most important player in my tennis career is leaving," the 36-year-old Spaniard said.
"At the end, this moment will be difficult. I'm super-excited and grateful to play with him."
Federer has struggled with a knee problem and does not feel able to play singles.
His last competitive match was a defeat by Poland's Hubert Hurkacz in last year's Wimbledon quarter-finals.
US Open semi-finalist Tiafoe, 24, says it will be "a special night" playing against Federer in the final match of his career.
"I'm just excited to play two up-and-comers," laughed the American.
"The crowd is obviously going to be for them. You understand that kind of moment, and just go out there and do your part and just try to get a win."
Team World captain John McEnroe said all of his team wanted to play against Federer, joking he needed to "flip some coins" to make his picks.
"[Jack and Frances] are opponents to a very unique situation that we are all fortunate enough to be around. This is like an incredible moment for our sport," said the seven-time major singles champion.
"The good news is that if they win, they are not going to be villains. This is about the celebration of what Roger has accomplished and him ending it and hopefully not hurting himself, is what I'm thinking."
Europe take on a world team in the three-day Laver Cup, where Italian Matteo Berrettini will take Federer's place over the weekend.
In Friday's day session, Norway's Casper Ruud faces Sock and Greek Stefanos Tsitsipas meets Argentine Diego Schwartzman in singles matches.
The 21-time Grand Slam winner Novak Djokovic is also on Team Europe, captained by Bjorn Bjorg, while Team World also includes American Taylor Fritz and Canadian Felix Auger-Aliassime.
The Laver Cup, named after Australian great Rod Laver, was Federer's brainchild and Europe have won all four previous editions of the event which sees a total of 10 singles and two doubles matches.
Each match win is worth one point on Friday, two points on Saturday, and three points on Sunday, with the first team to earn 13 points declared the winners.
The annual event, which started in 2017, is sanctioned by the ATP but does not carry ranking points for the players. Three players on each side are determined by the world rankings, with three others picked by the captain.
Federer poses for a selfie with team-mates in London
-- Courtesy of BBC News