On Tuesday, AstraZeneca said the studies were being paused while it investigated whether the adverse reaction was linked with the vaccine.
But on Saturday, the university said it had been deemed safe to continue.
Health Secretary Matt Hancock welcomed the news that the trials would resume.
"This pause shows we will always put safety first. We will back our scientists to deliver an effective vaccine as soon as safely possible," he added.
The university said in a statement that it was "expected" that "some participants will become unwell" in large trials such as this one.
It added that the studies could now resume following the recommendations of an independent safety review committee and the UK regulator, the Medicines and Healthcare Products Regulatory Agency.