In the same transfer window, Diego Costa and Cesc Fabregas joined Chelsea for a combined £52m, while Luke Shaw became the most expensive teenager in the world when Manchester United paid Southampton £27m for his services.
If Arsenal wanted value for money with their new Chilean maestro, they certainly got it. He played 166 games, scored 80 goals and racked up 46 assists. With those numbers, Alexis should be leaving Arsenal as a club legend, but the feeling is that his time in north London was unfulfilled.
"I'm so happy to be joining a club which has a great manager, a fantastic squad of players and huge support around the world," he said when he arrived four years ago. "I'm looking forward to playing in the Premier League and Champions League."
He won neither, though. While Sanchez lifted two FA Cups with the Gunners, his aim was to challenge for the biggest trophies and that is something Arsene Wenger’s side have failed to do over the past four years, culminating in last season’s dismal fifth-placed finish in the Premier League and subsequent demotion to the Europa League.
Sanchez had wanted to leave Arsenal since the back end of last season and that manifested itself on the pitch with regular acts of frustration towards his team-mates.
The forward was dropped for a game against Liverpool in March after storming out of an Arsenal training session in which he had been involved in a slanging match with some of his colleagues.
Laurent Koscielny, who is also Arsenal's vice-captain, was one of several players who called Sanchez out on his on-field shows of frustration, and it’s understood the two argued again after games against Burnley and Southampton this season.
The 3-3 draw against Bournemouth last January saw Sanchez throw his gloves on to the floor and storm off down the tunnel, while Arsenal’s passionate away supporters have previously criticised him for failing to show his appreciation for the fans.
Indeed, Goal published a video of Mesut Ozil after last season’s defeat against Chelsea which showed the German urging Sanchez and Nacho Monreal to salute the supporters while they were heading towards the tunnel at Stamford Bridge.
A frustrated Mesut Özil after the game shouts at Alexis Sanchez and Nacho Monreal for not going over to the Arsenal away supporters. pic.twitter.com/XAx8TghCHn— Chris Wheatley (@ChrisWheatley_) February 4, 2017
"Legend", proclaimed Sanchez when he was asked to describe Wenger in one word a season after joining the Gunners. The mutual respect between the two was partly behind Sanchez’s decision to join Arsenal and the Frenchman’s philosophy of backing his players had certainly never wavered when it came to his talismanic frontman.
It emerged that over Christmas that a relaxed Sanchez travelled back to Chile, where he spent Christmas Day with his family - which meant a 14-hour flight just days before Arsenal's match against Crystal Palace.
Wenger denied that his player had visited his homeland over the festive period, but sources close to Sanchez had shown Goal photos of the trip which proved otherwise, confirming that his recent sighting in Paris was due to his connecting flight back to London being from the French capital.
Wenger's loyalty to his player was perhaps admirable but the unscheduled trip was a further sign of petulance from a player who knew his Arsenal exit was just weeks away.
Indeed, his departure has long been inevitable. He even signed a contract with Manchester City on deadline day last summer but the document never made its way to the Football Association (FA) because of Arsenal’s failure to land Thomas Lemar as a replacement.
Sanchez has cut an isolated figure throughout his four years at the club. The Chilean lives with his best friend – an Argentine former futsal player he has known since his time at River Plate – and prefers the company of his two golden Labradors Atom and Humber over meals out with his Arsenal team-mates.
His girlfriend, Chilean actress Mayte Rodriguez, travels around the world and is mostly based in South America, which only adds to the isolation – something which Sanchez has no problem with. It’s this independence and determination to be the best which makes him the player he is today.
From the rocky streets of Tocopilla to becoming one of the highest-paid players in world football, Sanchez has endeared himself to Arsenal fans over the past few years with not only his strike-rate but his work-rate, paying back his £35m transfer fee in goals and graft.
Furthermore, while he will now strengthen a Premier League rival at Manchester United, there is a feeling that Wenger and the club are relieved to see the back of a player whose temperament and behaviour has long suggested that he no longer wanted to wear the badge he kissed as recently as pre-season.
The break-up will hurt Arsenal more than it hurts Alexis but that is precisely why they are both now better off without one another.