The B-listed building, which has lain empty for more than 30 years, has been bought by marine engineering consortium, Malin Group.
They plan to create offices at the Pacific Quay site, with social and recreational space on the ground floor.
News of the redevelopment has been welcomed by Glasgow City Council leader Gordon Matheson.
He said: "This is very welcome news for the river and the city, and a vote of confidence in both.
"It seems very fitting that a Scottish marine engineering firm should choose such an iconic location on the Clyde for this key part of their future development."
John MacSween, managing director at Malin Group, which has offices in Sandyford Place, off Sauchiehall Street, said they were "very excited" about the move.
He said: "We are providing our staff base here in Glasgow with a spacious, state of the art building to operate from.
"The building's marine and industrial heritage, along with the very highly technical work we do, will make for an interesting combination."
Work is expected to begin on the conversion after the Tin Forest Festival - a production by the National Theatre of Scotland in the Rotunda and part of the Commonwealth Games Cultural Festival - has ended.
A spokesman for Malin said 25 to 30 staff would be housed in the Rotunda and it could take a year before the offices are ready.
The firm is expected to sell its current premises.
Pamela Grant, director at Pacific Quay Developments, said the area was an unrivalled business location because of its riverside setting and "the fact that it is within walking distance of the city centre."
The South Rotunda has lain empty since 1980 when the old Clyde Tunnel was closed to the public.
It enjoyed a brief boost during the 1988 Garden Festival and again in 1990, during Glasgow International Year of Culture.