Galashiels Academy will become the fourth TSIT site, following new facilities at Oriam in Edinburgh, Moray Sports Centre in Elgin and the King George V sports complex in Dumfries.
As well as the tennis centre, the new facility will also feature two canopy-covered padel courts, providing a further boost for the fast-growing sport in the Scottish Borders.
The £64m Galashiels Academy community campus opened to pupils in January.
SBC leader Euan Jardine said the new centre would allow people of all ages to get active while also providing facilities for “rising stars” to train and play locally.