Phones4U founder John Caudwell said the numbers fleeing the country amid Russia's invasion were "staggering and harrowing".
The businessman is offering refugees accommodation in a two-bedroom coach house on the grounds of his home at Broughton Hall near Eccleshall, between Stafford and Market Drayton, for "as long as they need it".
Posting on Instagram, he urged other wealthy individuals to follow in his footsteps and "step up and offer shelter" as he took aim at the UK's response to the conflict.
Mr Caudwell, who was born in Birmingham and grew up in Staffordshire, said: "It’s heartening to see how countries neighbouring Ukraine have opened their arms to this tidal wave of desperation. Particularly Poland, itself quite a poor country, which has already received more than a million people.
"By contrast, the British response is becoming embarrassing. I have no idea whether this is bureaucracy gone mad or something more nefarious, but we need to do much better.
"Apparently, if you don’t have family here, the other main visa route is to have a British sponsor. I don’t know how you become a sponsor, but consider this my application if it’s needed. I'd like to host a #Ukrainian family to live on the grounds of my estate in Staffordshire.
"I'll house them in their own, two-bedroom apartment in this coach house, providing all utilities and food as long as they need it. Although refugees will benefit from the safety and shelter I can provide, I suspect the experience will be unique, humbling and deeply enriching for me as well.
"I consider this a small gesture and my humanitarian duty. As Eastern Europe struggles to address the worsening crisis, I urge wealthy individuals to step up and offer shelter in their homes."
The businessman sold Phones4U, which was once Europe’s leading privately-owned mobile phone group, for £1.5 billion in 2006.
He has since set up a number of philanthropic projects including Caudwell Children, a children’s charity.