The trust had been rapped over the way it investigated patient deaths with calls for Katrina Percy to resign.
An investigation commissioned by NHS England found only 272 of the 722 deaths in the trust over the previous four years were dealt with properly.
But Ms Percy will continue in her role, interim chair Tim Smart has said.
In April, inspectors said the trust was "continuing to put patients at risk".
Then in June, the trust accepted responsibility for the death of 18-year-old Connor Sparrowhawk, who drowned in a bath at one of its facilities - Slade House in Oxford.
It admitted it "caused" the death of Connor - who had suffered an epileptic seizure before he died in July 2013 - and offered his family Â£80,000 compensation.
Following a six-week comprehensive review however, Mr Smart said it was clear the executive team had been "too stretched to guarantee high quality services".
He recommended the trust should "transform the way in which it delivers services, and makes changes to the structure and strength of its leadership team".
"[I am] satisfied that whilst the board should have acted in a more united way, I have found no evidence of negligence or incompetence of any individual board member," he said.
Regarding Ms Percy, he said she had been "too operationally focused" and this would be shifted to oversee the "delivery of the future strategy of the trust, which I believe needs to be accelerated".
Southern Health NHS Foundation Trust covers Hampshire, Dorset, Wiltshire, Oxfordshire and Buckinghamshire.
The chief executive of the much-criticised Southern Health NHS Foundation Trust will keep her job, it has been announced.