Hasselbaink, 44, was filmed as part of an investigation alleging corruption in football, apparently negotiating a fee to travel to Singapore to speak to a fake Far East firm.
He was also alleged to discuss possibly signing players from them.
The Rs said a lack of evidence from the newspaper ended their investigation.
"The club contacted and communicated with all the major parties involved, including The Telegraph, who failed to provide the club with the information previously requested," said a statement on the club website.
"Despite a number of requests from both the club and Jimmy Floyd Hasselbaink's legal team for the information relating to the inferences made on September 28, including video footage and a full transcript of the discussions that took place, nothing has been forthcoming.
"As a result, and in the absence of any further evidence, the board fully back Jimmy and his explanations relating to these inferences."
The Telegraph's investigation saw both Sam Allardyce leave his post as England manager and Barnsley assistant boss Tommy Wright sacked last month.
The League Managers' Association has previously accused the newspaper of holding up the investigation by not releasing evidence, while City of London Police also confirmed discussions had already taken place with the Football Association and the paper.
A Telegraph spokesperson said last month it remained their intention to release the information but that the police had asked to review it first.
"Jimmy openly admitted he was naive and, as such, has been reminded of his roles and responsibilities as manager of Queens Park Rangers," the QPR statement added.
"He remains fully focused on his job, and he does so with the board's unanimous support."
Former Chelsea and Netherlands striker Hasselbaink had always denied any accusations of wrongdoing.
QPR have said they fully back manager Jimmy Floyd Hasselbaink after completing their investigation into claims made by the Daily Telegraph.