Last year's Puskas award was won by Olivier Giroud, who hit a stunning scorpion kick to round off a superb team move for Arsenal against Crystal Palace in the Premier League.
For the first time in 12 years, Messi was not among the finalists with third place going to Salah for his incredible 44-goal debut season with Liverpool that carried the Reds to the Champions League final.
Messi and Ronaldo were the only winners of world soccer's main individual award from Federation Internationale de Football Association in various guises since 2008, both winning five titles each.
"This trophy is not just mine", the 33-year-old playmaker said.
"These things were not a burden, they only further motivated me", Modric said at the World Cup.
The Fifa Fan Award went to Peru's supporters who caused absolute scenes (in a good way) in Russian Federation this summer as the national team made their way to their first World Cup tournament in 36 years.
"He was my big inspiration and that team gave us belief that we could achieve something great in Russian Federation". You see the goalkeeper stranded in the middle there.
Real Madrid's Belgium global Thibaut Courtois won the Goalkeeper of the Year Award.
During a ceremony on Monday evening, Mo was awarded the Puskás Award for best goal scored in 2018 to honour his strike against Everton where he finished into the top right-hand corner from an incredibly tight angle.
France's World Cup-winning manager Didier Deschamps took the Men's Coach of the Year award, with compatriot Reynald Pedros claiming the women's award after winning the Champions League with Lyon.
Thibaut Courtois won the best goalkeeper award for helping Belgium reach the World Cup semi-finals as well as the FA Cup with Chelsea before a summer move to Madrid.
Peru's supporters won the FIFA Fan Award and German Lennart Thy, who plays for Turkish club BB Erzurumspor, won the FIFA Fair Play Award after donating stem cells to help a leukemia patient. Thy donated blood to enable doctors to generate stem cells that could make a transplant possible for a leukemia patient and possibly save their life.