The 22-year-old will sign a five-year contract, Barca said in a statement on their website after reaching an agreement with the Italian club to sign the player for €26 million (Dh137.3m).
The deal could rise to €37.5m depending on appearances and add-ons.
Sanchez, who will be the first Chilean to play for the club, will undergo a medical test, sign the contract and be presented at Camp Nou on Monday.
Sanchez has played for Udinese since 2008 and last season was voted the best player in Serie A, after scoring 12 goals in 31 games.
The player had also been linked with English sides Manchester United and Manchester City, but said last month that he wanted "Barcelona or nothing".
"[He] has been sought by the best teams in the world. However, he has been strongly committed to playing for Barca," the statement said.
Pep Guardiola, the Barca coach, said this week that his priority for the upcoming season was signing a forward, with Sanchez his top target.
"He is a very young player, can play in three attacking positions, has a lot of intensity in defence, very vertical, unbalancing, and from what I've been told he's a very good guy," he told a news conference on Tuesday.
The signing is the first of the new season for Barca, where Sanchez will join the likes of Argentine star Lionel Messi and Spain's David Villa.
Guardiola has also said is not giving up the fight to sign the midfielder Cesc Fabregas from Arsenal despite the determination by the Gunners' boss Arsene Wenger to hold on to his captain.
"There is still time," before the pre-season transfer window closes on August 31.
"We will try to reach a deal" on the 24-year-old, he said.
The club start their pre-season tour of the United States with a friendly against Manchester United in Landover, Maryland on July 30.
The Spanish league kicks off on August 21, where Barcelona visit Malaga.