Chelsea could pay up to £89m for Mudryk, making it the largest transfer fee received by a Ukrainian club.
The 22-year-old has signed an eight-and-a-half-year contract at Stamford Bridge.
Shakhtar will also play a friendly with Chelsea at their currently abandoned 50,000-capacity Donbass Arena in Donetsk when the war is over.
In an open letter released on the club's website on Monday, Shakhtar president Rinat Akhmetov said: "First of all, I want to thank the whole civilised world for helping Ukraine."
"Thanks to the Ukrainian army, the Ukrainian people and the huge support of the entire civilised world, we can talk about Ukrainian football today. Only together we will defeat the evil that has come to our home.
"I have mixed feelings today. On the one hand, I am happy for Mykhaylo and proud of him. This guy proved by his own example that the impossible can become possible thanks to talent and hard work. I am absolutely sure that all of Europe will applaud Mykhaylo's bright, beautiful playing.
"On the other hand, I have never hidden that my dream is to win European trophies. This means that players like Mudryk should be invited to our club, our Ukrainian championship, and win European trophies with such players, and not cheer for them, even when they play in the best clubs in the world.
"Unfortunately, this is not possible now, because there is a vile, unjust war waged against us by the Russian Federation in Ukraine. But I am convinced that we will win. And we will play a friendly match with Chelsea at Donbas Arena in Donetsk, Ukraine. We must do everything possible to bring this day closer.
"That is why I decided to launch the "Heart of Azovstal" project – to help the defenders of Mariupol and the families of fallen soldiers. Their feat has no analogues in modern history. It is thanks to them, their sacrifice and courage in restraining the enemy in the first months of the war that today we all feel the inevitability of the Victory of Ukraine.
"Today, I allocate 1 billion hryvnias to help our soldiers and defenders, as well as their families. They will be aimed at various needs – from treatment, psychological assistance, prosthetics to the implementation of targeted requests.
"In order to comply with the principles of transparency, a professional, independent team will be formed, which will interact with the defenders of "Azovstal", their families, patronage services, and volunteers. We are in eternal debt to our soldiers!"
