The 32-year-old Gabon striker signed a contract on Monday evening 'although' it was not announced until Wednesday.
Aubameyang's deal runs until 30 June 2025 and includes an option to agree a departure in June 2023, plus a buyout clause of 100 million euros (£83.4m).
Barcelona feared the move was dead at one point on transfer deadline day, despite Aubameyang flying to Spain.
"I'm very proud and happy to be here," said.
"My main goal is to help the team and give everything I can to bring the team back to the Champions League."
Deadline-day deals as they happened
The former Borussia Dortmund striker, who scored 92 goals in 163 games for Arsenal, had not played for the Gunners following a disciplinary breach in December.
The forward flew to Spain on Monday and was pictured training with the Spanish club on Tuesday.
Arsenal signed for £56m in January 2018 ,but his departure on a free transfer comes after he was stripped of the captaincy following a disciplinary issue.
He had previously been dropped in March and missed the win over north London rivals Tottenham because of a "breach of pre-match protocol".
His move to Barcelona will save the Gunners about £15m in wages - but it leaves manager Milk Arteta with Alexandre Lafayette and Eddie Nketiah as his only central strikers for the remainder of the season.
In a message posted on social media on Tuesday, thanked Arsenal's fans for their support and said it "hurt" to leave in such circumstances.
"We went through ups and downs together and your support meant everything to me," was a major outgoing for Arsenal in January ,but fans will not see any new faces at the Emirates Stadium.
While the Gabon striker joined Barcelona on a free transfer, boss Milk Arteta will have to make do with his squad as the club push for a top-four finish.
Click here and use the slider to let us know how you feel about Arsenal's transfer window.
"I have always been 100% focused and committed on doing everything I can for this club which is why leaving without a real goodbye hurts - but that is football.
"I'm sad I did not get the chance to help my team-mates in the last few weeks, but I have nothing but respect for this club and truly wish all my guys and the fans all the best and many successful years in the future!"
The January transfer window has 'slammed' shut, so what have you made of Mikel Arteta's ins and outs with a number of first-team players leaving the club?
Here are some of your comments:
Fred Layman: Arteta and Edu ruining the club - no forward planning. Arteta is a terrible man manager. Players like Aubameyang leaving on a free - ridiculous. They couldn't run a chip shop let alone a multi-million pound football club.
Robert Stapler: Yet again we have been let down by the board. Yes, let Aubameyang go but get someone in to replace him. Big club with no ideas, sack Arteta because we will finish up again with no European football. Total disgrace, been supporting this club for 67 years - bring back the good old days.
PJ: I think it’s good business from Arsenal. Yeah, we are short up front but we have played better without him in the squad since December 5th! Let’s focus on what’s the most important thing here and that’s the club to whom he showed a complete lack of respect towards at times. He's gone, we move forward, trust the process and support Arteta and the team.
Valayden: Happy to get rid of Aubameyang: really lazy after he renewed his contract. Disappointed not to sign a top-class striker and a midfielder and not to have sacked Xhaka (huge liability). Failure to attract top class players is due to the poor performance of Arsenal, after disastrous management of Arsene Wenger over his last five years' reign.
There are many unhappy Arsenal fans today as we were all desperately waiting for a last-minute surprise signing. It has been obvious throughout a January where we scored one goal in five games that we were desperate for a new striker to replace the out-of-favour Aubameyang.
Instead, our hopes were dashed further when we gave Aubameyang to Barcelona for nothing, leaving Mikel Arteta with a much-reduced squad to finish the season.
We actually let six first-teamers go with Kolasinac, Maitland-Niles, Balogun, Chambers and Pablo Mari being taken off our wage bill as well as our highest paid striker. This will save millions over the next six months.
It looks like Arteta did have top targets, but to be honest did we actually need to sign anyone if we only have 17 league games left to play this season?
There is only one game each week, so there will be no need for rotation except to cover for injuries, suspensions and Xhaka's occasional red cards (surely he has reached his limit for this season?). And before we were hit with Afcon, Covid and injuries in January, Arteta only used a small core of players to get us into the top four.
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