Barcelona reached agreement with Liverpool on the transfer of Luis Suarez, giving the troubled striker a chance to rehabilitate his image when his latest biting ban is over.
Suarez will travel to Barcelona next week for a medical and to sign a five-year contract.
"We would like to thank Luis for his contribution and the role he played in helping bring Champions League football back to Anfield,'' Liverpool said in a statement on its website.
The Uruguay international is prevented from any involvement in football until the end of October after being handed a four-month suspension by FIFA for biting an Italian opponent at the World Cup in Brazil.
When Suarez is eventually eligible to play again, Barcelona will be able to deploy a formidable front line also including Lionel Messi and Neymar, as the club rebuilds under new coach Luis Enrique after its first season without a major trophy in six years.
Sanchez becomes Gunner
Arsenal have completed the signing of Barcelona striker Alexis Sanchez, the Premier League club said.
No fee was disclosed but Arsenal are believed to have paid in the region of $59.56 million for the 25-year-old Chile international who joined Barca from Udinese in 2011.
Alexis will add power, creativity and much quality to our squad and we are all looking forward to him joining up with us in a few weeks.
"As many people have seen during the World Cup this summer, Alexis is a fantastic footballer and we are delighted that he is joining us at Arsenal Football Club," the club's manager Arsene Wenger said.
"Alexis will add power, creativity and much quality to our squad and we are all looking forward to him joining up with us in a few weeks."
The clubs had already reached a deal in principle but were ironing out personal terms for the player who was deemed surplus to requirements at Barca by new manager Luis Enrique despite him scoring 39 goals in 88 appearances for the Catalans.
Liverpool miss out
Sanchez's move to London will be a blow to Liverpool who were hoping to sign him as part of a deal taking Luis Suarez in the other direction.
"I'm looking forward to meeting my new team mates and to be playing for Arsenal in the Premier League and Champions League," Sanchez said.
Sanchez was a key member of the Chile team that shone in Brazil, reaching the World Cup last 16 before losing to the hosts on penalties. He scored two goals in four appearances.
Arsenal's lack of striking prowess has been blamed for their failure to challenge for the Premier League title since the departure of Robin van Persie to Manchester United in 2012.
Their total of 68 goals from 38 matches was the lowest of the top four last season with Frenchman Olivier Giroud top scoring in the league with 16.