Work has been ongoing at Morriston Hospital since September with the aim of keeping surgery waiting times down.
Abertawe Bro Morgannwg University Health Board said one of the factors behind longer waiting times in the past had been a lack of beds for people after surgery.
The extension will add four more critical care beds.
Health Secretary Vaughan Gething visited the hospital on Tuesday to see the final stages of the redevelopment, which is due for completion later this month.
He said the Welsh Government investment followed recommendations and feedback from clinical staff in Morriston.
"I'm pleased that more people will be able to benefit from high quality care closer to home," he said.
"We have made progress in reducing cardiac waiting times and are now investing to increase capacity in Wales."
Figures released by the Society for Cardiothoracic Surgery in 2015 ranked Morriston's unit sixth out of 39 for survival rates between April 2011 and March 2014.