Andy Begley's appointment needed the approval of the authority's councillors at its full meeting today to go ahead.
The motion was passed unanimously and the council's leader, Councillor Peter Nutting, said Mr Begley would "do a brilliant job in moving this council forward".
Councillor Nutting said he "could not speak highly enough" of the former executive director of adult social care, public health and housing, adding he was "really pleased at the appointment".
Mr Begley was one of the two-person joint interim chief executive team that replaced Clive Wright after his decision to leave the council earlier this year.
He had jointly held the post alongside Karen Bradshaw, the authority's executive director of children’s services.
Councillor Madge Shineton, a member of the council's Independent Group, also welcomed the move, having worked with Mr Begley on a number of occasions on the Health Scrutiny Committee,
She said: "He has his feet on the ground and has a detailed grasp of the county and its needs at the moment."
When he was selected last month, Mr Begley said he was was looking forward to taking on the job, and praised the efforts of staff throughout the pandemic.
He said: "I’m really proud to be taking up the position of chief executive at Shropshire Council and would like to thank the councillors for their offer and faith in me.
"Having worked as one of the interim chief executives for the best part of six months, I’d like to take this opportunity to praise and thank all the staff at Shropshire Council for their efforts throughout the floods and pandemic.
"I have been humbled by the coming together of the council, and look forward to leading the council through these challenging times and back into the good times."