WEF Founder and Executive Chairman Klaus Schwab declared the summit open amid the ski-resort receiving record snowfall.
Schwab welcomed members from business, politics, academia and media as well as the first timers with a round of applause.
He also said all are here despite such weather as "we are all part of a community".
"Participants are here because they are part of a multi- stakeholder community. No stakeholder alone can address the complex global agenda effectively," Schwab said.
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The Pope passionately called upon participants to overcome fragmentation between states and institutions and work together to facilitate more inclusive approaches in an increasingly globalised world.
In a speech delivered by Cardinal Peter Kodwo Appiah Turkson, Prefect of the Dicastery for Promoting Integral Human Development, Pope Francis said, "It is vital to safeguard the dignity of the human person, in particular by offering to all people real opportunities for integral human development and by implementing economic policies that favour the family".
Railway Minister Piyush Goyal, Andhra Pradesh Chief Minister N Chandrababu Naidu, Reliance Industries Chairman Mukesh Ambani, PepsiCo CEO Indra Nooyi and IMF Managing Director Christine Lagarde, among others, were present.
The winners of WEF's Crystal awards -- cine star Shah Rukh Khan, music icon Elton John and Hollywood actor Cate Blanchett -- were also in attendance.
More than 3,000 world leaders from business, politics, art, academia and civil society would be participating in the summit and the the Indian presence is the largest ever with over 130 participants.
Modi is the first Indian Prime Minister to attend Davos meeting in about 20 years since H D Deve Gowda in 1997.
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