World champion Barshim succeeds retired Jamaican sprint legend Usain Bolt. He claimed the title from a shortlist comprising Britain's long distance star Mo Farah and South Africa's 400m champion Wayde Van Niekerk.
Thiam, who won hepatathlon gold at the Olympics and worlds in London, beat off competition from Ethiopia's 10,000m Olympic champion Almaz Ayana and Greek polevault star Ekaterini Stefanidi.
The men's and women's finalists were whittled down from an original list of 10 by a vote of IAAF council members, fans and fellow athletes.
At the awards ceremony in Monaco Bolt was awarded the president's prize.