"Both were great servants to Motherwell and brought us considerable success."
Former Motherwell players Gary McAllister, the former Leeds and Coventry manager, Chris McCart, head of youth development at Celtic, and Luc Nijholt, assistant to Co Adriaanse at Red Bull Salzburg, have been linked with the Fir Park vacancy already, as has Queen of the South boss Gordon Chisholm.
"The task begins to find a new manager," continued Boyle's statement.
"This will be done on a timely basis and we will quickly address what arrangements can be put in place to look after the team during the early European campaign."
Motherwell begin pre-season preparations on 22 June, ahead of their involvement in the Europa League qualifying rounds.
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