The region’s record points scorer succeeds cyclist Geraint Thomas, who won in 2014, as BBC Wales Sports Personality of the Year, becoming the third Osprey to win the award.
Shane Williams collected the award in 2008, 11 years after Scott Gibbs received the accolade.
Results of a public vote were revealed at the Wales Sport Awards in Cardiff where BBC Cymru Wales and Sport Wales celebrated Welsh sporting success.
The Wales football team were named team of the year award after qualifying for the Euro 2016 finals and their manager Chris Coleman is the elite coach of the year.
Biggar reacted to the award by saying: "I'm so thrilled to bits that enough people voted.
"I'm very, very privileged to receive this and thank you everyone for voting.
"There are some great names on there and it's scary to think that mine name is on there with them.
"It doesn't feel right but I'm very, very pleased."
Biggar gave outstanding performances for Wales during the Rugby World Cup, the Six Nations and for his region.
The 26-year-old scored 23 points in a man-of-the-match performance in the 28-25 win over England in the pool stage at the World Cup, including a long-range winning penalty.
In total he scored 56 points in four matches as Wales were knocked out in the quarter-finals against South Africa.
In the 2015 Six Nations, he scored 26 points in five games as Wales missed out on the Championship on points difference with four wins from five. He also helped Ospreys to the semi-finals in the Pro12.
Biggar secured the public vote ahead of second-placed Geraint Thomas and world flyweight boxing champion Lee Selby.
Thomas became the first British rider to win the formidable E3 Harelbeke race in Belgium in March and as a key member of Team Sky helped Chris Froome claim his second Tour de France title.
Selby became the 12th Welsh world boxing champion by beating Russia's Evgeny Gradovich to claim the IBF featherweight title and defended his crown against Mexican Fernando Montiel in the USA.
The other nominees chosen by an expert panel for BBC Cymru Wales Sports Personality 2015 had been footballers Gareth Bale and Ashley Williams, triathlete Non Stanford, taekwondo competitor Jade Jones and Para-athlete Aled Sion Davies.
Everybody at the Ospreys would like to offer Dan our congratulations on achieving such a fantastic award.