The former Cardiff City striker penned a three-year deal this morning.
Bothroyd's signature marks a change in fortunes for manager Warnock, who has been thwarted in his attempts to bring in reinforcements so far this summer.
But despite his frustrations, Warnock says he is delighted to finally get his man.
"In bringing Jay in, we have managed to secure an excellent player which augers well for the forthcoming campaign," said the QPR boss.
"We have been chasing him for a number of weeks and it has been frustrating at times.
"We have had to have a lot of patience with this but, as the saying goes, good things come to those who wait.
"We are now working hard to add another new face to the squad and we hope to have that done very soon."