On 10 July 2014, Sánchez signed for Arsenal on a long-term contract for an undisclosed fee, reported to be around £35 million. Sánchez was given the squad number 17, previously worn by Nacho Monreal, who took the vacant number 18 instead. In a statement released by the club, Sánchez said that he was "so happy to be joining Arsenal, a club which has a great manager, a fantastic squad of players, huge support around the world and a great stadium in London." Arsène Wenger praised Sánchez, saying that the Chilean international "has consistently produced top-quality performances at the highest level for a number of seasons now and we are all excited to see him integrate into the Arsenal squad." Sánchez made his first appearance for Arsenal on 2 August 2014, as a substitute during a 5–1 win against Benfica in the pre-season Emirates Cup tournament.

His first competitive appearance was against Manchester City in the Community Shield, on 10 August, playing in the first half and helping Arsenal to a 3–0 win. On 16 August, he made his Premier League debut against Crystal Palace, assisting Laurent Koscielny's equaliser in a 2–1 home win. He scored his first goal for Arsenal on 27 August, slotting the ball past Beşiktaş goalkeeper Tolga Zengin in stoppage time of the first half to secure a 1–0 aggregate victory and a spot in the group stage of the Champions League. Following the game, Wenger was full of praise for Sanchez, with the Arsenal boss saying: "He had a good game, not only on the technical side but on the fighting side. He was mobile, dangerous and has shown as well he has great fighting spirit, qualities that will be very important in the Premier League." His first league goal came four days later, netting the opening goal in a 1–1 draw away to newly promoted Leicester City. He then scored his second League goal in as many games against previous season champions Manchester City, demonstrating perfect technique to sidefoot a volley high past Joe Hart in a 2–2 draw at the Emirates.

Alexis scored his fourth goal for Arsenal, from a free-kick, as the Gunners fell to 1–2 defeat to Southampton in the Capital One Cup. He scored his first goal in the Champions League proper for the Gunners on 1 October, netting Arsenal's third goal of their 4–1 home win over Galatasaray and also provided assists for two goals by Danny Welbeck. On 18 October, Alexis scored the opening goal and later assisted a late Danny Welbeck equalizer in a 2–2 draw against Hull City at home. The following league fixture saw him scoring a brace against Sunderland after capitalizing on errors made by Wes Brown and former Arsenal keeper Vito Mannone.On 1 November, Sánchez again scored a brace, this time against Burnley, thus helping the Gunners to a 3–0 victory. With that brace Alexis scored his 9th and 10th goal of the season for Arsenal.

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