Like-for-like sales grew 6.4% in the final three months of the year, and were up 4.2% in the year as a whole.
The Newcastle-based baker added full-year results were set to be "slightly ahead" of its previous expectations.
However, Greggs added that rising costs this year were likely to have a "modest impact" on profit margins.
"Looking forward there is greater uncertainty in the trading environment with increased pressure on real income growth," it said.
"We also continue to expect some industry-wide cost pressures in 2017 and these are likely to have a modest impact on margins in the short term."
Greggs said its takeaway food range had been "the main driver of sales" during the year, including its Balanced Choice range, which it markets as being a healthier option.
The company now has 1,764 shops, having opened 145 outlets during 2016 - including 56 franchised stores - and closed 79.
High Street baker Greggs has reported "strong" Christmas sales, with takeaway food, mince pies and its Festive Bake pie proving popular.