"We have received a clearance from the government to rebuild the stadium," said K. Mathivanan, a member of Sri Lanka Cricket's interim committee.
"We plan to finish construction by August and that will allow us to play one Test there when South Africa come."
South Africa, scheduled to tour Sri Lanka in August for two Tests, were the last team to play a match at Galle before the December 2004 disaster.
The tsunami destroyed the stadium's main pavilion, including dressing-rooms, and also severely affected the indoor nets.
Australian leg-spinner Shane Warne, former Australian captain Steve Waugh and former England all-rounder Ian Botham visited the stadium after the disaster and pledged their support to rebuild it.
Galle is a happy hunting ground for Sri Lanka, who have won six of their 11 Tests at the venue.