He applied to Swansea Council for permission to keep using the first floor of the garage as an office.
Today, councillors on the authority's planning committee voted to give him temporary permission for two years despite being advised to refuse consent.
Among eight letters of objection received by councillors was one from a solicitor representing Zeta Jones's parents, Dai and Pat, who are believed to be about to move into the property and have their own property on the market, and CZ Investments.
It says: "Our clients purchased the plot and agreed to the construction of a substantial dwelling on the clear understanding that it would be private, prestigious and exclusive and extremely safe and secure as it was a 'gated' development."
It goes on: "Our clients would also be extremely concerned and alarmed that the privacy and security of the development would be jeopardised by virtue of the visits to site by members of staff, customers and delivery vehicles of Mr Gwynn."
But a letter written on behalf of Mr Gwynn claimed that the fact the estate, in the fishing village of Mumbles, was set to be home to Zeta Jones while she was in Wales was attracting about seven parties of sightseers every day, even in winter.
"It is not unusual to have a minibus pull up at the site entrance," it says. "Many of these visitors have travelled some considerable distance, including mainland Europe."
It adds that the "disruption" is expected to increase once the family moves in.
Mr Gwynn's representative also told councillors that during an average week the business received just three visits from a courier, with the number sometimes going down to one.
Council officials told members of the planning committee that the isolated nature of the garage and the lack of windows meant that using it as an office would not harm the privacy of neighbours.
But the councillors were advised to turn down the application because officers deemed the potential for additional comings and goings would seriously
undermine the character of the residential area and that approval would set "an undesirable precedent".
Councillor Howard Morgan told the committee today that during a site visit by councillors to the estate last month, a group of foreign tourists were gathered outside.
"You would think they had come to visit a shrine," he said.
Urging fellow committee members to allow the application, the councillor added: "We should just think of this as three houses for Joe Bloggs and his neighbours."
The committee's decision to grant permission will now be referred for approval by the full council, with a recommendation for temporary consent for two years.
After today's meeting, Mr Gwynn said: "This means we can continue to work and three people's jobs are now safe for two years. Common sense has obviously prevailed."