Arteta has scored two goals in three matches so far this season
The deal had looked dead earlier after talks between the two clubs broke down but Arteta handed in the transfer request an hour before the deadline.
Arsenal also signed Chelsea's Yossi Benayoun, 31, on a season-long loan.
"Mikel indicated to me that he wished to join Arsenal if a bid came in," said Everton manager David Moyes.
"I am very disappointed to lose him but the prospect of Champions League football was something I wasn't able to offer him."
Arteta joined Everton from Real Socieded for £2m in 2005 and has scored 35 goals in 208 appearances.
He started his career with Barcelona before spells with Paris Saint-Germain FC and Rangers.
The Spaniard suffered a knee ligament injury in February 2009 and was sidelined for almost 12 months before signing a new five-year deal in August 2010.
Former Arsenal defender Martin Keown told BBC Sport that both Arteta and Benayoun were "solid signings".
MARTIN KEOWN'S VIEW
"I think back to the [Dennis] Bergkamp era, the impetus those players brought. Arteta is a great passer, Benayoun is not getting into Chelsea team. It's a mixed bag for Arsenal fans."
Benayoun, the Israel captain, wrote on social networking site Twitter: "I sign with Arsenal, very happy and excited about it, but now my head is only in the game against grecce on Friday, thanks for the support."
Both clubs later confirmed the move had gone through.
Chelsea offered Liverpool £8m plus Benayoun for Reds midfielder Raul Meireles on Tuesday, but that deal was rejected.
He joined Blues from Liverpool for £5m in July 2010 but was restricted to 10 appearances last season because of an Achilles injury and has seen only one minute of action this time round.
It had been rumoured Benayoun would be included in an offer from Chelsea for Tottenham playmaker Luka Modric.
Newcastle had also been linked with the Israeli.
Denmark striker Nicklas Bendtner completed a move away from Emirates Stadium just before the window closed, joining Sunderland on a season-long loan.
Arsenal
have signed Everton's Mikel Arteta for £10m after the Spanish
midfielder submitted a transfer request to force through the move.
Arteta, 29, joined the Gunners on a four-year contract just before the transfer window closed.The deal had looked dead earlier after talks between the two clubs broke down but Arteta handed in the transfer request an hour before the deadline.
Arsenal also signed Chelsea's Yossi Benayoun, 31, on a season-long loan.
"Mikel indicated to me that he wished to join Arsenal if a bid came in," said Everton manager David Moyes.
Benayoun's well-worked goal against Burnley
Arteta joined Everton from Real Socieded for £2m in 2005 and has scored 35 goals in 208 appearances.
He started his career with Barcelona before spells with Paris Saint-Germain FC and Rangers.
The Spaniard suffered a knee ligament injury in February 2009 and was sidelined for almost 12 months before signing a new five-year deal in August 2010.
Former Arsenal defender Martin Keown told BBC Sport that both Arteta and Benayoun were "solid signings".
MARTIN KEOWN'S VIEW
"Arsenal made eight signings during this transfer window,
which is the biggest turnover of players Arsene Wenger has sanctioned
since he came to the club back in 1998. He brought very well then, with a
big group coming in - Petit, Overmars, Garde, Manninger, Wreh. Lots
came in at once and we've not seen Wenger do that since. It hasn't
really been his style of management. The amount of players he has
brought in is a big call and only the results will tell as to whether or
not he has got the right blend."
Read more from Martin Keown
But when asked if they would be adequate replacements for the
departed Cesc Fabregas and Samir Nasri, Keown added: "No they're not,
it's very hard to replace those players.Read more from Martin Keown
"I think back to the [Dennis] Bergkamp era, the impetus those players brought. Arteta is a great passer, Benayoun is not getting into Chelsea team. It's a mixed bag for Arsenal fans."
Benayoun, the Israel captain, wrote on social networking site Twitter: "I sign with Arsenal, very happy and excited about it, but now my head is only in the game against grecce on Friday, thanks for the support."
Both clubs later confirmed the move had gone through.
Chelsea offered Liverpool £8m plus Benayoun for Reds midfielder Raul Meireles on Tuesday, but that deal was rejected.
He joined Blues from Liverpool for £5m in July 2010 but was restricted to 10 appearances last season because of an Achilles injury and has seen only one minute of action this time round.
It had been rumoured Benayoun would be included in an offer from Chelsea for Tottenham playmaker Luka Modric.
Newcastle had also been linked with the Israeli.
Denmark striker Nicklas Bendtner completed a move away from Emirates Stadium just before the window closed, joining Sunderland on a season-long loan.