The crossing was shut between 2am and around 9pm yesterday after the northbound vehicle crashed onto the southbound carriageway.
The incident damaged around 40m of steelwork in the centre of the bridge, which engineers have been working to repair.
It was feared that the work would take several days and involve lane closures.
The lorry was removed by late afternoon but hopes the crossing could be re-opened in time for yesterday’s evening rush hour were dashed.
Police have confirmed that the lorry driver, who suffered minor injuries, has been charged because high-sided vehicles were banned from the bridge at the time.
The incident caused ten-mile traffic queues through Fife during the morning rush hour after commuters diverted to the Kincardine and Clackmannanshire bridges.
Paying tribute to engineers, transport minister Humza Yousaf said: “Once again, the Forth Road Bridge team has stepped up to repair the bridge.
“They have successfully removed the overturned HGV and carried out temporary repair work to the damaged central reserve safety grille on the bridge.
“I would like to pay tribute to the engineers and workers who have faced up to some very challenging and difficult weather conditions throughout the day, to complete the work and get the bridge reopened as quickly and as safely as possible.
“The bridge is now open in both directions for traffic, subject to any restrictions the weather may bring, in line with the forecast.
“The closure of the bridge was the result of an HGV driver ignoring travel advice and restrictions for high-sided vehicles using the bridge during a period of severe weather warnings. Thankfully no one was hurt in this incident, but a great deal of disruption has been caused.”
He added: “There are and will continue to be a number of severe weather warnings in place for the next few days.
“So, this is a timely reminder of the importance of listening to advice, checking travel bulletins before travelling and obeying VMS messaging, road restrictions and signed advice.
“Conditions over the coming days will inevitably lead to some difficult driving conditions.
“Gritting teams will be out across the period to help keep the trunk roads moving. Gritters will also be patrolling at strategic locations on the network to make sure that they can respond to any emerging issues.
“Key routes are being monitored across our network of weather stations and live cameras and the Traffic Scotland National Traffic Control Centre will take all of this information and send it out to road users through the website and Traffic Scotland twitter feed on a 24/7 basis.
“We would ask that people keep the conditions in mind when they are making their travel plans and leave plenty of time. We are making as much information available as possible to allow the public to make informed decisions. The winter treatments page on the Traffic Scotland website has details of which routes are being treated and our Trunk Road Gritter Tracker lets road users see where gritters have been out in the last 24 hours.
“Travel operators’ websites will have all of the relevant information on ferries, rail and air and Traffic Scotland has a web page with all of these links.”
Mark Arndt, Amey’s operating company representative for the Forth Road Bridge, said: “It’s been a challenging day but our team has put in a tremendous amount of effort to get the HGV off the bridge and complete the repair work while battling with strong winds, rain and sleet. We’re pleased that the bridge has now been reopened but we are mindful that with adverse weather forecast for the coming days, there may be further restrictions.
“We’d urge drivers to check our website or the Traffic Scotland twitter feed for up-to-date travel information before they start their journey.
“And, of course, we’d strongly recommend that road users comply with any restrictions.”