The 26-year-old agreed his first dual contract in March and the new deal has an option which could see him stay until the 2019 World Cup, according to the Welsh Rugby Union (WRU).
Biggar is the first of Wales' 17 dually contracted players to re-sign.
"Hopefully others will follow suit and we can continue to grow a strong player base in Wales," said Biggar.
"It's taken a little while to get to the point where everyone is happy with the deal, but I'm glad to have the next couple of years sorted and I can continue to play for Wales and week in, week out for the Ospreys."
Biggar's current deal was due to expire at the end of this season.
Ospreys are also eager to secure the future of Wales lock Alun Wyn Jones and scrum-half Rhys Webb.
Both players signed dual contracts this season, and Ospreys captain Jones has said he is "weighing up" his options.
Dual contracts are 60% funded by the WRU and 40% by the region.
Ospreys and Wales fly-half Dan Biggar has signed a new national dual contract.