Union Aslef announced on Monday that members had voted to take industrial action in a dispute over pay.
They say tram drivers are paid significantly less than train drivers but the company has failed to make an “acceptable” pay offer.
The union has not announced a strike date but legally it must occur within 28 days of the ballot.
A spokesman for FirstGroup said it was “very disappointed”.
“We’re very disappointed Aslef has taken this ballot for strike action, which was taken against the recommendation of union negotiators, and in spite of the fact that we believed we had arrived at a suitable settlement with union members,” he said.
“A strike will bring massive disruption to customers.
“We ask Aslef to continue to join us around the table to seek a solution that will bring this dispute to a satisfactory conclusion for everyone.”
Around 100 Croydon Tramlink staff are members of Aslef. The turnout for the ballot was 82 per cent and the result was 100 per cent in favour of a strike.
The union says its members “earn much less than those doing similar jobs in other parts of the industry”.
A tram driver is paid around £36,000, significantly less than train operators on the London Underground or staff working for the Docklands Light Railway (DLR).
Croydon Tramlink is operated by FirstGroup on behalf of Transport for London (TfL).
Aslef said the company cut pension benefits last year costing staff up to £120 per month – “much more” than the pay rise they had been offered.
A spokesperson said: “We are prepared to keep talking to resolve this dispute, but unless FirstGroup listens to this unanimous message from Aslef members, then strike action may become inevitable.”