They continued their success with a historic home win over the All Blacks in the autumn worldwide series.
The awards capped a triumphant month for the squad, which included Ireland's first ever home win against the All Blacks.
Since taking on the job in 2013, New Zealander Schmidt has overseen the team's most successful period, winning three Six Nations titles, and enjoying victories over the All Blacks and a series triumph in Australia, among others.
Up next for Sexton may be an away trip to Rodney Parade and a game with Dragons in the Guinness PRO14.
IRFU chief executive Philip Browne said: "Andy has world class coaching credentials and we are pleased to have a roadmap for an orderly transition post-Rugby World Cup to the 2020 Six Nations".
Head coach Schmidt is set to announce his decision on his long-term future next week, with the Kiwi expected to return to his native New Zealand after the 2019 World Cup.
SA Rugby president Mark Alexander praised Springbok winger Aphiwe Dyantyi for scooping the World Rugby Breakthrough Player of the Year Award in association with Tudor at a glittering function in Monaco on Sunday evening.
"You don't have to worry about that, we'll do that", Sexton said.
"The close working relationship that our current coaching group have and what they will continue to gain over the next year with Joe still at the helm leaves Andy and Irish Rugby in the enviable position of having continuity before building the road forward".
"I look at the nominees and any one of them would have been a worthy victor". "I've committed to a certain time-frame with them and I've stuck to that".
Sexton became only the second Irishman after hooker Keith Wood to win the award. "Any of them would have been a worthy victor".
Australia's only award victor was referee Angus Gardner, crowned referee of the year.
Perry Baker of the United States was Men's Sevens Player of the Year and New Zealand's Michaela Blyde was Women's Sevens Player of the Year.
World Rugby Women's Player of the Year - Winner - Jessy Tremouliere (France).
Jamie Armstrong of charity The Clan was handed the Spirit of Rugby Award, while Stephen Moore and DJ Forbes both picked up the International Rugby Players (IRP) Special Merit Award.