Bjoerndalen, 40, beat the previous record he shared with compatriot and cross-country skier Bjorn Daehlie.
Bjoerndalen, who also has 19 world championship titles to his name, won his first medal at the Nagano Games in 1998 and has claimed at least two medals at every Olympics since then.
He also won the 10km sprint gold in Sochi.
Bjoerndalen, who started in the World Cup 20 years ago, was one of three members of the Norway relay to shoot clean in another dominant performance.
He had come close to winning his 13th medal in the 20km individual last week but had to settle for fourth. He dropped out of contention in Tuesday's mass start when he made four mistakes in the final shooting.
Image: Ole Einar Bjoerndalen
Photograph: Harry How/Getty Images
Sochi Olympics: Pussy Riot crashes Russia's party; Norway strike gold
Winter Olympics 2014: Stars to look out for in Sochi
Himanshu Thakur ready for flag to fly at closing ceremony
Sochi Olympics: Criticism of Games reflects 'Cold War' mentality, says Putin
Which countries have budgets bigger than India? Find out...