Federer, the second seed who won five years in succession at Flushing Meadows from 2004-2008, starts against Leonardo Mayer, the 34th-ranked Argentine.
The 34-year-old Federer won the pair's only other meeting in Shanghai last year but had to save five match points in the process.
Federer has not been back to a US Open final since losing the 2009 title match to Juan Martin del Potro and was a semi-final loser in 2014.
But he made the Wimbledon final again in July and a victory over Novak Djokovic in the Cincinnati Masters final last month only served to boost his belief that he can add to his 17 majors, the last of which came at the All
England Club in 2012.
"I feel like I have a good chance but I really can't think further than my first-round opponent right now," said Federer.
"My focus needs to be not trying to win the tournament right away. That would be thinking too far ahead.
"I haven't been in the final in this tournament as of late. I came close but close is not good enough."
Murray, the 2012 champion, begins his campaign against controversial Australian Kyrgios, the world number 37.
Kyrgios is playing under the shadow of a suspension following his now-infamous, lurid tirade against Switzerland's Stan Wawrinka in Montreal.
Kyrgios was picked up by courtside microphones claiming that compatriot Thanasi Kokkinakis had slept with WTA player Donna Vekic, the girlfriend of Wawrinka.
The Australian was widely condemned for the outburst but Murray has pleaded for patience.
"He's a young guy," said Murray of his 20-year-old opponent who he has defeated three times in three meetings.
"He made a mistake," he said.
"All the guys here when they were 19 or 20 made mistakes."
Murray said it was unfortunate the incident happened and it was wrong.
But he added: "I don't think he's a bad guy. He's an unbelievably talented guy with a lot of potential."
Wawrinka, the fifth seed who made the semifinals in 2013, starts against Spain's Albert Ramos-Vinolas.