Alexis Sánchez has joined Manchester United from Arsenal, with Henrikh Mkhitaryan moving in the opposite direction.
The straight swap deal was confirmed by both Premier League clubs in statements published on their official websites on Monday evening.
Sánchez "thrilled" at Manchester United switch
"I am thrilled to be joining the biggest club in the world," said 29-year-old Chile international forward Sánchez.
"I have spent three-and-a-half wonderful years at Arsenal and I bring with me very positive memories of that great club and its fans.
"The chance to play in this historic stadium and to work with José Mourinho was something I could not turn down.
"I am very proud to be the first Chilean player ever to play for United's first team and I hope I can show our fans all around the world why the club wanted to bring me here."
Sánchez is expected to be the highest ever paid player in the Premier League, with British media reporting a pre-tax salary of £500,000 (567,000 euros) a week.
The deal that sees Armenia international winger Mkhitaryan, also 29, head to the Emirates following a mixed 18 months at Old Trafford had been expected for several days.
"Alexis one of the best attackers in the world" - Mourinho
Sánchez had joined Arsenal in 2014 for £31.7 million after three years at Barcelona.
"Alexis is one of the best attacking players in the world and he will complete our very young and talented group of attacking players," said United manager José Mourinho.
"He will bring his ambition, drive and personality, qualities that make a Manchester United player and a player that makes the team stronger and the supporters proud of their club dimension and prestige.
"I would like to wish Henrikh all the success and happiness that I am sure he is going to get. He is a player that we will not forget, especially for his contribution to our Europa League victory."
Mkhitaryan: Arsenal move "a dream come true"
Mkhitaryan joined United for around £30 million in 2016 after three years at Borussia Dortmund.
"I'm very happy that we could finish this deal and I'm very happy to be here," said Mkhitaryan.
"It's a dream come true because I've always dreamed of playing for Arsenal. Now that I'm here, I'll do my best for this club to create history."
Wenger: "Mkhitaryan has all the attributes"
Arsenal boss Arsene Wenger added: "Henrikh is a very complete player. He creates chances, he defends well, he can absorb distances and he's very committed as well.
"I must say he's a player who has all the attributes."