The rise will mean an increase of 32p per week for the average Band B home in the borough. The plans were approved as part of Telford & Wrekin Council's budget for 2013/14, which is designed to protect services, at a full council meeting last night.
Councillor Bill McClements, cabinet member for resources and service delivery, said the increase was necessary to allow the council to continue to provide essential services and help create more jobs.
But the tax hike was criticised by Conservative councillors, who said the tax increase was too high.
Councillor McClements said: "We need to prepare for large budget gaps in the years ahead. A 1.9 per cent rise is lower than inflation. We're not playing games with tax increases before and after an election – these are the most serious financial difficulties the council has ever faced."
Conservative Councillor Adrian Lawrence welcomed council investment, but added: "We think we should be keeping council tax increases to 0 per cent, following the lead of Shropshire Council. A 1.9 per cent increase is an 8 per cent increase over three years and a 20 per cent increase over 10 years."
The budget was passed by a majority vote.