In Bergkamp's second season at Inter, the club changed managers again, appointing Ottavio Bianchi. Bergkamp endured a disappointing campaign, troubled with stress injuries and fatigue from the 1994 World Cup. He managed to score 5 goals in 26 appearances. Off the field, Bergkamp's relationship with the Italian press and fans became uncomfortable. His shy persona and his propensity to go home after matches was interpreted as apathy. Because of his poor performance on the pitch, one Italian publication renamed their award given to the worst performance of the week, L'asino della settimana (Donkey of the Week) to Bergkamp della settimana. Inter ended the league season in sixth position and failed to retain the UEFA Cup, with the club eliminated in the second round. In February 1995, the club was purchased by Italian businessman and fan Massimo Moratti, who promised to invest heavily in the squad. Bergkamp's future in the first team was uncertain following the signing of Maurizio Ganz a month after the takeover.
As Moratti prepared to make wholesale changes at the club, Bergkamp left Inter and signed with Arsenal in June 1995 for a transfer fee estimated at £7.5 million. He became manager Bruce Rioch's first signing at Arsenal and broke the club's transfer fee record set at £2.5 million. Bergkamp's arrival at the club was significant not only because he was an established international footballer who looked to have his best years ahead of him, but also because he was a major contributor to Arsenal's return to success after much decline in the mid-1990s. On the opening day of the 1995–96 league season, Bergkamp made his full debut against Middlesbrough. He struggled to adapt to the English game and failed to score in the club's next six league matches, prompting ridicule by the national press. On 23 September 1995, Bergkamp scored his first and second goals for Arsenal against Southampton at Highbury. Bergkamp ended his first season with 33 appearances and 11 goals, helping Arsenal finish fifth and earn a place in the UEFA Cup by scoring the winner against Bolton Wanderers on the final day of the season.
During his time at Inter Milan, Bergkamp was switched to the position of a main striker, but failed to cooperate with his offensive partner Rubén Sosa, whom he later called "selfish". Furthermore, due to his introverted character, he was accused of lacking consistency and leadership skills by the Italian press, and struggled to replicate his previous form during his time with Inter. When Bergkamp joined Arsenal in 1995, he enjoyed a successful strike partnership with Wright, and in later seasons Anelka and Henry, playing in his preferred position as a creative second striker. The arrival of Overmars in the 1997–98 season enhanced Bergkamp's play, as he was getting more of the ball. Between August and October 1997, he scored seven goals in seven league matches. A similar rapport developed between him and Ljungberg during the 2001–02 season.