Wright signed for Arsenal in September 1991 for £2.5 million, which at the time was a club record fee. He scored on his debut against Leicester City in a League Cup tie, and then scored a hat-trick on his League debut against Southampton. He won the Golden Boot in his first season by scoring 29 league goals. He scored a hat-trick in the final game of the season against Southampton; his third goal being the last ever scored in the old First Division.
Wright went on to be the club's top scorer for six seasons in a row. He played a major part in the club's success during the 1990s, winning an FA Cup and League Cup double in 1993; he scored in both the FA Cup Final and the replay against Sheffield Wednesday. Wright also helped Arsenal reach the 1994 UEFA Cup Winners' Cup Final, although Wright was suspended for the final in which Arsenal beat Parma 1–0.

On 13 September 1997 he broke Cliff Bastin's Arsenal goalscoring record with a hat-trick against Bolton Wanderers (a record since surpassed by Thierry Henry in October 2005).

Wright scored a total of 185 goals for Arsenal in 279 starts and 9 substitute appearances. His final goal at Highbury came on 4 October 1997 against Barnsley and was his 300th career goal. He scored his final goal for Arsenal on 6 January 1998 in a League Cup quarter-final victory against West Ham United at the Boleyn Ground. In his absence, Arsenal were eliminated from the League Cup in the semi-final by Chelsea, ending their hopes of a unique domestic treble.
On 15 July 2008, he finished 4th in 50 Greatest Gunners listed on the Arsenal website.