"I'm leaving the best team in Spain to join the best team in England," Reyes said at a Seville news conference called to announce his departure.
"I'll always have Sevilla in my heart. It is a bittersweet day."
League leaders Arsenal issued a statement on their website confirming the deal, saying, subject to a medical, it was "a long-term contract for an undisclosed fee."
Sevilla president Jose Maria del Nido said his club had a agreed a confidentiality pact regarding the transfer fee but British media reported it to be around 20 million pounds ($36.26 million).
Arsenal's previous record was the 13 million pounds they spent to bring in French international striker Sylvain Wiltord in 2000 and manager Arsene Wenger has usually sought to spend the club's money in smaller deals for less-known players.
"It's the saddest thing we've had to do at Sevilla," Del Nido said. "We said we would only sell Reyes if we received an offer over and above his market price.
"The transfer is for more than Bayern Munich paid for (Roy) Makaay, more than Barcelona paid for Ronaldinho and more than Real Madrid paid for (David) Beckham."
Arsenal, who are still in contention for four trophies, have been in search of a striker to cover for Thierry Henry.
Manager Arsene Wenger has a host of talented youngsters to call on for domestic cup games, but it is the depletion in the senior ranks that is causing concern - particularly with the resumption of the Champions League next month.
Nigerian international Nwankwo Kanu has departed for the African Nations Cup, youngster Jeremie Aliadiere is recovering from a knee ligament injury while Wiltord has suffered a setback in his recovery from an ankle injury.
"We have a game based on movement, technique and pace, Reyes has all that," Wenger said. "He is a fantastic signing."
"He can play as a striker, on the left or the right. In fact, anywhere as an offensive player."
OUTSTANDING DISPLAYS
Reyes made his Sevilla debut as a 16-year-old in 2000 and started receiving widespread attention in the 2001-2002 season.
He scored eight league goals last season as he made it to the fringe of the full Spanish international squad with a string of outstanding displays from the right side of attack.
Sevilla, currently 15th in the Spanish league, managed to fend off interest from some of Europe's biggest clubs, including a reported 15-million-euro approach from Arsenal, and with speculation about a move raging, Reyes signed a new seven-year contract in July.
He made his full international debut against Portugal in a friendly in September and went on to play in three qualifying games for Euro 2004, scoring twice.
The cost of Beckham's move from Manchester United before the start of the current season was 25 million euros ($31.3 million), plus up to 10 million euros ($12.52 million) depending on Real's performances in the Champions League over the next four years.
