ATP world number one Djokovic beat fellow nominees Lewis Hamilton, LeBron James, Kylian Mbappe, Luka Modric and Eliud Kipchoge to claim the award for the fourth time – only Roger Federer has won it more.
The rejuvenated Serbian recovered from a loss of form and persistent elbow injury to win Wimbledon and the US Open in 2018, earning a return to the top of the rankings.
"A Laureus Award is what every athlete wants to win, and this one is a huge honour for me," Djokovic said. "Being among so many sporting greats here tonight, and hearing about the inspirational work Laureus is doing around the world, gives this Award a special meaning for me.
"Last year was an incredible season for me, returning from injury to win Wimbledon and the US Open is something I'll remember forever. I am delighted and I would like to thank the Laureus Academy for their support."
Biles became the first woman to win a fourth all-around title at the 2018 World Artistic Gymnastic Championships.
The American claimed a record-breaking four golds – she has now amassed an unprecedented 14 at the worlds – in Doha and added one silver and a bronze.
Naomi Osaka received the World Breakthrough of the Year award after claiming her first grand slam title at the US Open, while Didier Deschamps accepted the prize for World Team of the Year on behalf of FIFA World Cup winners France.
Former Arsenal boss Arsene Wenger was given the Lifetime Achievement award and Cesc Fabregas, Alessandro Del Piero, Luis Figo and Fabio Capello were among those to give him a guard of honour at the ceremony in Monaco.
Skiing great Lindsey Vonn received recognition for her illustrious career in the shape of the Spirit of Sport Award.