Ahead of the meeting, Allardyce has hit out at a lack of "decency" after Everton pushed ahead with boardroom changes by appointing Professor Denise Barrett-Baxendale to replace Robert Elstone as CEO with Dr Keith Harris becoming deputy chairman without his knowledge.
'Sam was brought in at a challenging time last season to provide us with some stability and we are grateful to him for doing that.
'Again, we'd like to place on record our honest thanks to Sam for his work with us over the last few months and wish him well for the future'.
The 63-year-old came out of retirement last year to take charge of an Everton side under desperate circumstances and guided them to an eighth place finish in the Premier League.
Allardyce has another year left on his contract, but met the club's major shareholder Farhad Moshiri on Wednesday morning when his departure was confirmed. "The catalyst for this decision is that unwarranted approach, something which the board believes has seen a significant deterioration in both focus and results to the point where the long-term future of Watford FC has been jeopardised".
Whoever is appointed, Stubbs says they face a huge summer as they look to amend the mistakes Everton made in previous transfer windows, having had little to show for the nearly £300million spent since Farhad Moshiri's takeover.
"They must have been in the pipeline for a considerable time but no one thought to tell me and my staff".
The Toffees offered as much as £12m in compensation for Silva but their approach was rebuffed.
A mediation meeting last month between the two clubs - and instigated by the Premier League - failed to resolve the highly acrimonious dispute.