Clive Wright, who has held the position since November 2012, said he did not wish to comment on the decision – taken at a group meeting of Conservative councillors on Monday evening.
The decision will come as a shock to many, with the council currently in the grip of dealing with its worst flooding crisis of more than 20 years, and also looking to the construction of some huge multi-million pound infrastructure projects over the coming years.
In a message to staff Mr Wright said that the decision had been agreed with council leader Peter Nutting.
He also paid tribute to the efforts of council staff who have been battling floods across the county.
He said: "I have agreed with the leader that I will leave my post as chief executive of Shropshire Council with immediate effect.
"I want to place on record my heartfelt thanks to all the amazing people I have worked with here at the council and our partners and communities. It has been a great privilege to serve you all and the people of Shropshire as chief executive.
"I am proud to have been part of the council and your exemplary response to the floods over the last eleven days demonstrates what being part of the public sector is about. Seriously, well done everyone!
"I wish you and the council all the very best for the future."
One source, who was present at the meeting where councillors decided they wanted to replace Mr Wright, said the matter had not met with unanimous approval.
They said: "There was a fairly deep divide in terms of opinion at the meeting last night."
The timing of the move was also described as "awful" and "very disappointing".
The decision represents the most significant shake-up at the top of the council since Councillor Nutting replaced Malcolm Pate as leader of the authority.
It is understood that senior members of the council's cabinet had wanted a change in the man at the top, and had pushed for the decision.
The move means both of the county's major councils – Telford & Wrekin and Shropshire, will have relatively new chief executives.
Richard Partington announced his decision to leave the Telford authority last year, with the council replacing him with David Sidaway.
Mr Wright's replacement will have a number of significant and pressing issues on the agenda.
They include plans for one of the county's major roads projects, the North West Relief Road in Shrewsbury, progressing a major overhaul of Shrewsbury's town centre and the future of Riverside and the shopping centres it bought for £51m, as well as significant development at Mile End in Oswestry.