Belichick wore a special shirt emblazoned with Ebner's USA Rugby number.
Ebner, who primarily plays special teams for the Patriots, was excused by the team to compete as part of the U.S. men's rugby sevens team in Rio. That event makes its Olympics debut Tuesday.
Ebner was an All-American in rugby at Ohio State before joining the Patriots in 2012.
"I also want to thank (the Patriots) and USA Rugby for giving me the opportunity to chase a dream I've had since I was a boy in a sport in which I've always had a passion," Ebner said of his opportunity to compete in Rio, according to ESPN's Adam Schefter. "I can't put into words how much this opportunity means to not only me, but my friends and family as well."
Ebner is scheduled to rejoin the Patriots at training camp after the the rugby sevens competition ends on Aug. 11.