The lifting of the ban for lorries over 7.5 tonnes at 11pm comes two weeks after they were permitted to cross overnight, northbound only.
The full re-opening comes more than two months after damage was found to the main span truss-end links, part of the support structure under the southbound carriageway.
It is a month earlier than expected, with transport minister Derek Mackay saying favourable weather had enabled the work to be completed earlier than expected.
Hauliers said the closure had had a “devastating” impact on some operators and lessons must be learned over bridge maintenance.
Mr Mackay said: “The immediate repair work is in the final stage and no further structural defects have been identified during painstaking investigations by engineers.
“I know that this is something that will be welcomed by the tens of thousands of drivers who use the bridge on a daily basis, especially the heavy goods vehicle drivers who have had to observe restricted crossing times in the past few weeks.
“I would like to thank them for their patience during this time and stress again that safety and the long-term integrity of the bridge had to be our main considerations.
Mr Mackay also praised the bridge workers working round the clock to complete the repairs. He said: “The team has worked tirelessly throughout despite very challenging weather conditions, employing innovative approaches to the repairs and putting in place very effective solutions to complex problems.”
Chris MacRae, the Freight Transport Association’s head of policy in Scotland, said: “While this is fantastic news for freight operators, we must not forget the closure caused severe disruption at the worst possible time of year.
“The financial impact for some operators was devastating.
“Lessons must be learned about the importance of maintaining critical national infrastructure like the bridge.
“We mustn’t get into a situation like this again.”
Scottish Labour deputy leader Alex Rowley said: “We must make sure the on-going maintenance is carried out to the level required and cost is not used as an excuse not to do whatever work is needed.”
Mr Mackay said monitoring systems installed on the bridge following the damage would be kept and a full “health check” of the structure had been carried out during the closure.