Four outdoor netball and tennis courts at a venue to be decided.
Both the Swansea Harriers' senior teams are in the UK's top 20 and Mr Owen said he was hopeful the investment would attract more youngsters to the sport.
The money will boost athletics
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"When Morfa closes we will be homeless for about a year and we will either go to Neath or use inferior indoor training facilities," added Mr Owen.
"But we are delighted that at last we are moving towards the future."
Swansea Council leader Lawrence Bailey said the money was a huge vote of confidence.
"This grant is a huge boost for Swansea," he said.
Start date
"It clearly demonstrates the confidence that Sportlot and the Sports Council for Wales have in our plans to create a sports village and regional athletics centre.
"It is also further proof that Swansea is becoming a leading sports venue in the UK.
"We have a new 50-metre national pool, the best 10km road race in Britain, we are going to host this year's British Triathlon Championships, create a sports village and move ahead with plans for the 20,000 all-seater Morfa Stadium."
There is still no official start for the Morfa Stadium development .
It is expected to take 12 to 14 months to complete.