The 22-year-old, who was announced by the Stamford Bridge club during their Premier League game with Crystal Palace on Sunday, had seemed set for north London as late as Thursday but it was always Chelsea's intention to go in big for the player, and they followed that through with offers that were simply too good to turn down.
The Independent has been told that Mudryk will be on over £100,000 a week, with Arsenal having initially gone up to £50,000 a week.
Shakhtar Donetsk were, meanwhile, intent on as high a fee as possible due to the aggravation that they had lost out on a lot of potential sales due to Fifa's ruling that foreign players could leave Ukraine for free after Vladimir Putin's invasion of the country.
While Arsenal valued the player, and there is some irritation within the club at how the manner their deal has been hijacked, the Premier League leaders were insistent there was a level they wouldn't go beyond.
Mudryk is seen as having a lot of current talent and future potential, but Arsenal do not believe that warrants going all in. They still want to make two signings in this window, and have been offered Brighton's Leandro Trossard. Barcelona's Raphinha has also come up as an option as the Catalan club again attempt to balance finances.
Chelsea have already added striker David Datro Fofana from Molde and centre-back Benoit Badiashile from Monaco in the January window, as Todd Boehly looks to give new boss Graham Potter the tools to turn around the team’s performance.
The addition of Mudryk will mean an initial outlay of over £100m from Chelsea this month, with more to follow in future if Mudryk’s additional payments are triggered.