In a statement, the council said that it has selected option 5A which would run from Crossbush Junction and reconnect with the A27 north of Walberton.
According to consultation documents, the selected route would have a "significant impact on the South Downs National Park and its setting".
"Due to the introduction of the new bypass, there would be noticeable damage to the park", the documents said.
The scheme would also have a "major adverse impact" due to the potential loss of ancient woodland.
However, West Sussex County Council said that the selected option would be acceptable "with the proviso that a package of environmental mitigation measures is introduced".
Bob Lanzer, the council’s cabinet member for highways and infrastructure, said: "Overall, the environmental impacts of Option 5A, if appropriately mitigated, are likely to be significantly outweighed by the substantial economic benefits of this option over the longer term.
"This is why, provided that a high-quality package of environmental mitigation measures is identified and delivered as part of the scheme, Option 5A is the council’s preferred option for an A27 Arundel bypass. It represents the best fit with the strategic outcomes that the council is seeking for the A27."
The council’s decision is in response to a consultation launched by Highways England on three possible options for the new road link.
The council said that a preferred route is expected to be announced this winter by the secretary of state. This would be followed by a further consultation ahead of the submission of a development consent order.