Mr Brown confirmed reports the bridge, which will cost up to £1.35 billion, would not be completed on schedule by the end of the year because of bad weather hampering construction.
He said it would be finished within the contractual completion date of June 2017 and the extra cost would be borne by the private sector contractors rather than the taxpayer.
This includes an extra 100 workers being taken on and longer working hours introduced to make up for lost time.
The setback has come despite a one-year contingency being included in the five-year construction project to allow for bad weather.
It will come as embarrassment to the Scottish Government, whose Transport Scotland agency has prided itself on getting other major roads projects like the M80 and M74 extension completed on time or early.
Mr Brown said the private sector consortium Forth Crossing Bridge Constructors (FCBC) told Transport Scotland last week it could not achieve the “target” opening date of December.
He said despite a series of bad weather delays since September, the consortium had believed until last month it could complete the job by then.
Mr Brown said: “However the impact of the weather in April and May was particularly severe, with 13 days and 12 days lost to weather respectively.
“As a result, FCBC have advised Ministers that due to the combined effects of the time lost in these two months, they can no longer deliver the December 2016 target opening date for the structure.”
The cabinet secretary said he had been assured during a site visit in March that the project was on schedule.
He said: “The contractors have now reached the stage where further additional resources will not bring the delivery date forward due to the complex technical nature of the construction work, which means that a complex sequence of operations must be used to complete this innovative structure.
“At this stage, the programme shows the Queensferry Crossing is now expected to be open by mid-May 2017, prior to the contractual completion date of mid-June 2017.
“We will continue to work closely with the contractors and I will personally ensure that every pressure and every resource is brought to bear to deliver or indeed to better this date.”
Mr Brown added: “The December 2016 target date was set to address concerns about the long term condition of the Forth Road Bridge, where it was originally believed that it would be restricted as early as 2017.
“These concerns have proven to be less immediate, and the recently installed structural health monitoring system is providing assurance on the ability of the bridge to sustain traffic.”
Mid Scotland and Fife Conservative MSP Murdo Fraser said: “This is very disappointing news for people on both sides of the bridge.
“They were continually told by the Scottish Government that this project was ahead of schedule and would soon be up and running.
“Now we find this is not the case, so the SNP must now give an exact date when this will be completed by.
“We saw the sheer disruption caused to people and businesses when the existing Forth Road Bridge was closed over Christmas.
“It’s essential we know whether or not the patch-and-mend approach taken at that point will be enough to ensure it can cope until the Queensferry Crossing opens.”
Scottish Labour deputy leader Alex Rowley said: “Today’s announcement will be greeted with disappointment in Fife and beyond.
“As someone who has campaigned for a new crossing for decades, whilst the delay is disappointing, we need to keep it in perspective and make clear this new bridge is good news for Fife, good news for the east of Scotland, indeed good news for the whole of the Scottish economy.
“That is why it is important that minsters do not announce unrealistic deadlines and it is crucial there is full transparency in this project.”