While the prime minister met airport staff and security, he bumped into Ronnie and Debbie Strickland from Fort Lauderdale, Florida, who were sitting in the departures lounge.
The couple, who have been married for 45 years, have been on a 25-day cruise and were waiting for their flight home when the PM arrived.
Debbie, 64, said: 'I totally wasn't expecting this - another lady noticed more security turning up and told us she thought there was a VIP coming through.
'Then a bunch of people in suits turned up, then you guys [the press] arrived with your cameras, so at that point we knew for sure that something was happening.
'I once saw President Bush get on a helicopter, but have never been able to talk to a president or prime minister before. It really was amazing.'
Ronnie, 69, added: 'This might be the best layover we've ever had, it was a total shock to see the prime minister turn up at a small airport like this.'
The nature of Mr Johnson's visit is not known, and due to the invite-only nature of the visit, the Local Democracy Reporting Service was unable to interview him.
There is some speculation that his visit could be connected to the airport's expansion plans, which would extend the runway by 164m at the northern end and add a 600-space car park.
The plans were approved by Eastleigh Borough Council, but is now awaiting ruling from the High Court.
Local councillors were unaware of the prime minister's visit and he does not appear to have done any campaigning, unlike Labour Party leader Sir Keir Starmer, who visited Southampton earlier in the week to campaign for the local elections.
Southampton is considered to be one of the key national battlegrounds for this year's elections, alongside Gosport.
In Southampton, the Conservatives are defending a majority of just two seats, and all seats are up for grabs in Gosport following a boundary restructuring.