The deal was put on hold by the Competitions and Markets Authority, pending an investigation into the potential for the acquisition to reduce competition in the UK vehicle salvage sector.
It feared that while Copart and Hills might not be direct competitors now, there was a chance they could be in the future.
However, after reviewing responses from customers, the CMA has provisionally reversed its decision.
Kirstin Baker, chair of the independent panel of experts conducting the most recent investigation, said: "We've gathered new evidence which means we no longer consider that this deal raises competition concerns in the vehicle salvage sector. We conduct these thorough investigations to fully understand issues affecting competition in that market. The purpose of the provisional findings stage is to gather responses and review the evidence before we make a final decision.
"In some cases, new evidence comes to light which causes us to change our mind as we have done here."
Jane Pocock, chief executive of Copart UK & Ireland, said: "This decision is testament to the thoroughness of the CMA process and reflects both the significant hard work of all the Copart teams involved and the unwavering support shown by our customers, both of which I am very grateful for.
"We are incredibly excited about the opportunity, and what it brings to our existing customers and of course to the wider market. Equally, we are looking forward to formally welcoming Ian Hill and his great team to the Copart family.
"We remain committed to our mission of ensuring that we serve our customers and the wider automotive sector by providing market leading green parts, total loss, and remarketing services."