After Chelsea's £50 million signing of Fernando Torres, it is the second biggest incoming transfer in British football history and almost trebles Arsenal's previous club record £15?million fee for Andrei Arshavin.
"While talking with Arsène Wenger I immediately felt what I had missed at last," Özil said. "This is 100 per cent faith in me. I want to help this club to finally win titles again.
"I am thrilled to be joining a club of the stature of Arsenal. It will be great for my own personal development as a player."
Arsenal's signing of Özil also capped a record-breaking window for English football, with the total spending of Premier League clubs reaching almost £600 million.
As well as Özil, Arsenal also enhanced their goalkeeping options by recruiting Emiliano Viviano on a year-long loan from Palermo.
The initial loan will cost £1 million and gives Arsenal an option to buy Viviano at the end of the season.
Viviano has won six caps for Italy but is being signed as back-up to Wojciech Szczesny and Lukasz Fabianski rather than as a new first-choice keeper.
Arsenal also spent much of Monday trying to complete a loan deal for Demba Ba but, with Chelsea demanding a fee of £3 million and unwilling to strengthen a direct rival, no agreement could be reached.
The failure to sign Ba ensured that Nicklas Bendtner remained at Arsenal, despite almost reaching a deal with Crystal Palace.
The signing of Özil, however, became the priority for Wenger, who has tracked the 24-year-old player ever since 2007 when he broke into the Schalke team as an 18-year-old.
Wenger had always said that he would be prepared to pay big money for what he calls "super quality" and, with Real Madrid keen to recoup some of their £86 million outlay for Gareth Bale, Özil became available. As well as the £42 million fee, Arsenal have broken their wage structure to sign Özil.
"We are extremely pleased," Wenger said. "He is a great player, with proven quality at both club and international level.
"We have watched and admired him for some time. I have said throughout the summer that we have been working hard to bring in top quality players to this football club. I have always had the full support of the club in making decisions on the football side."
Although the arrival of Özil represents a major step forward for Arsenal, there was still disappointment that the club failed to recruit the world class striker that had been the central aim of the window.
Bids were made for Liverpool's Luis Suárez and Gonzalo Higuain, who eventually joined Napoli from Madrid but the club were ultimately left trying to secure Ba on a temporary deal from Chelsea.
It all leaves Arsenal particularly reliant this season on Olivier Giroud. Yaya Sanogo has been added on a free transfer, while Lukas Podolski and Walcott are seen as potential alternatives in the centre forward's position. Bendtner will now be given the opportunity to rehabilitate himself at Arsenal.
Wenger was also determined to enhance his midfield options and will see Özil as the long-term successor to Cesc Fabregas in the playmaker's position behind the main centre forward. Tomas Rosicky, Wilshere and Santi Cazorla have been rotating in that role over the past two years but the team will surely now be rearranged around Özil.
Cazorla is likely to move to the left, while Wilshere will continue to compete with Aaron Ramsey, Mikel Arteta and Mathieu Flamini as one of the two holding midfielders.
Why Arsenal have been tracking the German
Arsène Wenger has been tracking Mesut Özil since 2007 and regards him as one of the most technically accomplished players in world football. It is his record for creating goals that has particularly attracted the Arsenal manager.
Özil has 94 assists over the past three years for Real Madrid and Germany. Cesc Fabregas, who was also regarded as a specialist provider of goals, has only 49 assists for Arsenal, Barcelona and Spain in that same period.
Özil has won 47 Germany caps and, after Per Mertesacker and Lukas Podolski, is the third member of Joachim Löw's national squad to join Arsenal over the past two years.