The Newmarket handler was one of a number across the town who had their horses tested after having a runner at the same meeting as one from the yard of Donald McCain, who has had three vaccinated horses test positive for the highly-contagious virus.
Tate, who ran Solar Park on Monday at Wolverhampton - where McCain saddled Dark Confidant - told Press Association Sport: "We've had our results back and we are all clear, which is a relief.
"We tried to get on top of the pile by getting the troops mobilised and getting the samples to the Animal Health Trust as quickly as possible.
"I was hoping to get them back last night - and I drive down there, but the gates were shut. So I was back at 8am this morning and was told they were all clear, which is good from my point of view - and for racing.
"I told David Sykes from the BHA (British Horseracing Authority), and he said 'that is the first bit of good news I've had today'."
While Tate - a qualified vet - has received his results, he believes the chances of racing resuming in Britain on Wednesday depend on how swiftly test results from other yards come back.
He added: "The Animal Health Trust is doing a great job working through the night to keep on top of it, but it depends if it can cope with the volume of samples between now and Monday.
"If the tests do come back all clear and everything gets done, then racing may resume on Wednesday - if not, it might be another day or two afterwards."
