The fee represents a significant jump from Arsenal's opening £30m bid, which Villa rejected earlier in the window as they held out for a valuation closer to £60m.
The two clubs found a compromise on Thursday, with Arsenal's improved offer including add-ons finally meeting Aston Villa's demands.
Konsa is unlikely to be involved when Mikel Arteta's side begin the defence of their Premier League title at home to Coventry on Friday, given the timing of the move. He could instead be in line to make his Gunners debut when Arsenal travel to Villa Park on August 31 for their next league fixture.
The move has been driven by a growing injury list at the back for Arteta, with William Saliba sidelined for several months after aggravating a back issue at the World Cup and Jurrien Timber still working his way back from the groin problem that forced him to miss the tournament altogether.
With Ben White and Cristhian Mosquera the only fit right-sided defenders currently available, Arsenal moved for Konsa to shore up their options before the new season gets fully under way.
The 28-year-old returned to Villa training this week following an extended post-World Cup break, having started every match for England at this summer's tournament in North America up until their semi-final exit. His versatility across the back line, along with his Premier League experience, made him Arteta's preferred target to address the club's defensive concerns, after Arsenal also explored a move for Bayer Leverkusen defender Jarell Quansah but were put off by the fee involved.
Konsa's departure represents a significant blow for Aston Villa, who face a fresh Champions League campaign this season and will now need to identify a replacement of their own in defence.
He joins Arsenal with two years still remaining on his previous Villa contract, meaning the deal comes with the club banking a substantial fee for a player who was not actively seeking an exit before Arsenal's interest crystallised in the closing weeks of the window.
Villa have already begun exploring alternatives at the back, with Chelsea's Tosin Adarabioyo among the names under consideration as a potential replacement.
For Arsenal, the addition of Konsa gives Arteta a proven Premier League defender capable of covering multiple positions just as his existing options at the back are stretched thin heading into a title defence.