The merger creates the world's fourth-largest car company, but has raised concerns about continuing investment at Vauxhall.
Unite national officer Des Quinn said he wanted an urgent meeting to "alleviate uncertainty".
Vauxhall has 3,000 staff in the UK, the bulk at its Ellesmere Port plant.
Fiat Chrysler and PSA, which also owns Peugeot, Citroen and Opel, confirmed a $50bn (£30.8bn) merger deal on Wednesday.
The companies said the deal is aiming for annual cost savings of $4bn through shared purchasing agreements and combined technologies.
The companies say there are no plans to close factories. But when it emerged earlier this year that the two firms were in negotiations, there was speculation that Vauxhall was vulnerable to any restructuring.
Mr Quinn said: "Unite is seeking guarantees at the highest level as to the long-term future of all PSA's UK sites and its highly skilled world class workforce.
"It is essential that such a meeting happens as soon as possible in order to alleviate the natural and legitimate concerns of the workforce at this time of change and uncertainty."
He said the popularity of Vauxhall and Fiat cars in the UK meant there was industrial logic about maintaining a UK presence.
PSA boss Carlos Tavares will become chief executive of the new company and will also have a seat on its board.
The deal is Fiat Chrysler's second attempt at a merger this year.